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The eccentricity of the curve represented by the equation x2 + 2y2 – 2x + 3y + 2 = 0 is

Solution for the question - the eccentricity of the curve represented by the equation x2 + 2y2  2x +3y + 2 = 0 is '/>   '/>   '/>  0

The eccentricity of the curve represented by the equation x2 + -Turito

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The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are

Solution for the question - the foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are (-1, 2), (-1, -6).(1, -2), (1, - 6)

The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are-Turito

The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is

Solution for the question - the eccentricity of the ellipse 9x2 + 5y2  30y = 0 is none of these'/>   '/>   '/>

The eccentricity of the ellipse 9x2 + 5y2  30y = 0 is-Turito

The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is

Solution for the question - the sum of all possible numbers greater than 10,000 formed by using{1,3,5,7,9} is 19686660000

The sum of all possible numbers greater than 10,000 formed by u-Turito

Number of different permutations of the word 'BANANA' is

Solution for the question - number of different permutations of the word 'banana' is 503540

Number of different permutations of the word 'banana' is-Turito

Given : Two functions <img src="data:image/png;base64,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" class="Wirisformula" alt="A equals left curly bracket a comma b comma c comma d right curly bracket" width="95" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mo»=«/mo»«mo»{«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»,«/mo»«mi»c«/mi»«mo»,«/mo»«mi»d«/mi»«mo»}«/mo»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="B equals left curly bracket 12 comma 34 right curly bracket" width="92" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»B«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1,2«/mn»«mo»,«/mo»«mn»3,4«/mn»«mo»}«/mo»«/math»'/> One-to-One functions define that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B). Each element of set A will pair with one element from set B and other elements of set A cannot pair with the paired element of A. Thus, number of one - one function is 4! =  24

The number of one - one functions that can be defined from <img src="data:image/png;base64,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" class="Wirisformula" alt="A equals left curly bracket a comma b comma c comma d right curly bracket" width="95" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mo»=«/mo»«mo»{«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»,«/mo»«mi»c«/mi»«mo»,«/mo»«mi»d«/mi»«mo»}«/mo»«/math»'/> into <img src="data:image/png;base64,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" class="Wirisformula" alt="B equals left curly bracket 12 comma 34 right curly bracket" width="92" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»B«/mi»«mo»=«/mo»«mo»{«/mo»«mn»1,2«/mn»«mo»,«/mo»«mn»3,4«/mn»«mo»}«/mo»«/math»'/> is

Solution for the question - the number of one - one functions that can be defined from into is 261824

The number of one - one functions that can be defined from into-Turito

When a die is rolled number of possible outcomes is selecting an event from 6 events = <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 6 subscript 1" width="28" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»6«/mn»«/mmultiscripts»«/math»'/> When four dice are rolled number of possible outcomes = <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 6 subscript 1" width="28" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»6«/mn»«/mmultiscripts»«/math»'/>x <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 6 subscript 1" width="28" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»6«/mn»«/mmultiscripts»«/math»'/>x <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 6 subscript 1" width="28" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»6«/mn»«/mmultiscripts»«/math»'/> x <img src="data:image/png;base64,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" class="Wirisformula" alt="C presuperscript 6 subscript 1" width="28" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«none/»«mn»6«/mn»«/mmultiscripts»«/math»'/> = <img src="data:image/png;base64,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" class="Wirisformula" alt="6 to the power of 4" width="18" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»6«/mn»«mn»4«/mn»«/msup»«/math»'/>  Thus, four dice are rolled then the number of possible out comes is <img src="data:image/png;base64,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" class="Wirisformula" alt="6 to the power of 4" width="18" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»6«/mn»«mn»4«/mn»«/msup»«/math»'/>.

Four dice are rolled then the number of possible out comes is

Solution for the question - four dice are rolled then the number of possible out comes is '/>   '/>   '/>   '/>

Four dice are rolled then the number of possible out comes is-Turito

<h2 class="Solution_html__KkUW2"><img src="data:image/png;base64,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" class="Wirisformula" alt="T o t a l space n o. space o f space w a y s space i n space w h i c h space a space g a r l a n d space c a n space b e space m a d e space o f space n space t h i n g s space i s space fraction numerator left parenthesis n minus 1 right parenthesis factorial over denominator 2 end fraction" width="560" height="37" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»T«/mi»«mi»o«/mi»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»o«/mi»«mo».«/mo»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»w«/mi»«mi»a«/mi»«mi»y«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»w«/mi»«mi»h«/mi»«mi»i«/mi»«mi»c«/mi»«mi»h«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»a«/mi»«mi»r«/mi»«mi»l«/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»m«/mi»«mi»a«/mi»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»i«/mi»«mi»n«/mi»«mi»g«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mfrac»«mrow»«mo»(«/mo»«mi»n«/mi»«mo»§#8722;«/mo»«mn»1«/mn»«mo»)«/mo»«mo»!«/mo»«/mrow»«mn»2«/mn»«/mfrac»«/math»'/></h2>Thus , the number of ways in which 5 different coloured flowers be strung in the form of a garland is : <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator open parentheses 5 minus 1 close parentheses factorial over denominator 2 end fraction space equals space fraction numerator 4 factorial over denominator 2 end fraction space equals space 12" width="153" height="37" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mn»5«/mn»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mo»!«/mo»«/mrow»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mn»4«/mn»«mo»!«/mo»«/mrow»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»12«/mn»«/math»'/>

The number of ways in which 5 different coloured flowers be strung in the form of a garland is :

Solution for the question - the number of ways in which 5 different coloured flowers be strung in theform of a garland is : 2216

The number of ways in which 5 different coloured flowers be str-Turito

The letter CHEESE contains 3 E's Thus, Total number of arrangements of the letters of the word CHEESE = Number of arrangements of 6 things taken all at a time, of which 3 are of one kind = <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 6 factorial over denominator 3 factorial end fraction space equals space 120" width="78" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»6«/mn»«mo»!«/mo»«/mrow»«mrow»«mn»3«/mn»«mo»!«/mo»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»120«/mn»«/math»'/>

Number of ways to rearrange the letters of the word CHEESE is

Solution for the question - number of ways to rearrange the letters of the word cheese is 120119115

Number of ways to rearrange the letters of the word cheese is-Turito

The number of ways in which 17 billiard balls be arranged in a row if 7 of them are black, 6 are red, 4 are white is

Solution for the question - the number of ways in which 17 billiard balls be arranged in a row if 7 ofthem are black, 6 are red, 4 are white is '/>   '/>

The number of ways in which 17 billiard balls be arranged in a -Turito

The word MATRIX is a 6 letter word Thus, number of permutations that can be made using all the letters of the word MATRIX is 6! = 720

Number of permutations that can be made using all the letters of the word MATRIX is

Solution for the question - number of permutations that can be made using all the letters of the wordmatrix is 720480

Number of permutations that can be made using all the letters o-Turito

The number of different signals that can be made by 5 flags from 8 flags of different colours is :

Solution for the question - the number of different signals that can be made by 5 flags from 8 flags ofdifferent colours is : 5^(b) '/>   '/>   '/>

The number of different signals that can be made by 5 flags fro-Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end fraction" width="265" height="43" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mi»A«/mi»«mo»+«/mo»«mfrac»«mrow»«mi»B«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»C«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«msup»«mrow»«mo»)«/mo»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/> then A-B=

Solution for the question - if (x^(2)+x+1)/(x^(2)+2x+1)=a+(b)/(x+1)+(c)/((x+1)^(2)) then a-b= 4c+13c2

If (x^(2)+x+1)/(x^(2)+2x+1)=a+(b)/(x+1)+(c)/((x+1)^(2)) then a--Turito

Solution for the question - (x+1)/((2x-1)(3x+1))=(a)/(2x-1)+(b)/(3x+1) , then 16 a+9b= 865

(x+1)/((2x-1)(3x+1))=(a)/(2x-1)+(b)/(3x+1) , then 16 a+9b= -Turito

If <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction" width="339" height="44" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»10«/mn»«mi»x«/mi»«mo»+«/mo»«mn»13«/mn»«/mrow»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mfenced separators=¨|¨»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»6«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»A«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»B«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»K«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/math»'/> then K=

Solution for the question - if (x^(2)-10 x+13)/((x-1)(x^(2)-5x+6))=(a)/(x-1)+(b)/(x-2)+(k)/(x-3) thenk= -4-3

If (x^(2)-10 x+13)/((x-1)(x^(2)-5x+6))=(a)/(x-1)+(b)/(x-2)+(k)/-Turito

Dividend = Divisor <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==" class="Wirisformula" alt="cross times" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#215;«/mo»«/math»'/> Quotient + remainder f(x) = g(x) <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==" class="Wirisformula" alt="cross times" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#215;«/mo»«/math»'/> q(x) + r(x) f(x) = (x+1)<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==" class="Wirisformula" alt="cross times" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#215;«/mo»«/math»'/>  q1(x) + 7 f(-1) = 7 f(x) = (x-1) <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==" class="Wirisformula" alt="cross times" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#215;«/mo»«/math»'/> q2(x) + 3 f(1) = 3 f(x) is divided with <img src="data:image/png;base64,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" class="Wirisformula" alt="x squared space minus 1" width="50" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»-«/mo»«mn»1«/mn»«/math»'/> Let remainder be ax + b and quotient  be q3(x) <img 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class="Wirisformula" alt="f left parenthesis x right parenthesis space equals space left parenthesis x squared space minus space 1 squared right parenthesis space cross times space q 3 space left parenthesis x right parenthesis space plus space a x space plus space b
f left parenthesis x right parenthesis space equals space left parenthesis x space plus 1 right parenthesis left parenthesis x minus 1 right parenthesis space cross times q 3 left parenthesis x right parenthesis space plus space a x space plus space b
f left parenthesis negative 1 right parenthesis space equals space minus a space plus space b space equals space 7
f left parenthesis 1 right parenthesis space equals space a space plus space b space equals space 3
S o l v i n g space b o t h space t h e s e space e q u a t i o n s
b space equals space 5 space a n d space a space equals space minus 2
R e m a i n d e r space a x space plus space b space equals space minus 2 x space plus space 5" width="298" height="161" style="vertical-align:-81px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«msup»«mn»1«/mn»«mn»2«/mn»«/msup»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mi»q«/mi»«mn»3«/mn»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#215;«/mo»«mi»q«/mi»«mn»3«/mn»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»7«/mn»«mspace linebreak=¨newline¨/»«mi»f«/mi»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»3«/mn»«mspace linebreak=¨newline¨/»«mi»S«/mi»«mi»o«/mi»«mi»l«/mi»«mi»v«/mi»«mi»i«/mi»«mi»n«/mi»«mi»g«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mi»o«/mi»«mi»t«/mi»«mi»h«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»h«/mi»«mi»e«/mi»«mi»s«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»q«/mi»«mi»u«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mi»b«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mi»R«/mi»«mi»e«/mi»«mi»m«/mi»«mi»a«/mi»«mi»i«/mi»«mi»n«/mi»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»5«/mn»«/math»'/>

If the remainders of the polynomial <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis" width="29" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»'/> when divided by <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAANCAYAAADFVhxbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYBhYoAbEtUB8gWGQgcVAnAbE/2lt0X9a6EsG4g4s4s1QuQFzGAicA2JxJH4iEE8Z6BADAQ8g7oOyXYB472CIShjYDcT20JwiTISBhDDVHFYAxL+AWG+wJH4QsAbiNdDojBwsDlMC4k1AzAXEPEB8hoiopLnDRIF4G5pDfKAF4IA5jA2I1wGxNBa55dCcSssCmZzMMnAAAExeMnZLoJj8AAAAXXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbWF0aD4PWQOIAAAAAElFTkSuQmCC" class="Wirisformula" alt="x plus 1" width="38" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math»'/> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAANCAYAAADFVhxbAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ1JREFUeNpjYBhYoAbEtUB8gWGQgcVAnAbE/xkGKcDrsGQg7sAi3gyVGzCHgcA5IBZH4icC8ZSBDjEQ8ADiPijbBYj3DoaohIHdQGwPzSnCRBhICFPNYQVA/AuI9QZL4gcBayBeA43OyMHiMCUg3gTEXEDMA8RniIhKmjtMFIi3oTnEB1oADpjD2IB4HRBLY5FbDs2ptHQQOZll4AAAcYUqfhczavUAAABddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPng8L21pPjxtbz4tPC9tbz48bW4+MTwvbW4+PC9tYXRoPuKTcfIAAAAASUVORK5CYII=" class="Wirisformula" alt="x minus 1" width="38" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/math»'/> are 7,3 then the remainder of <img src="data:image/png;base64,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" class="Wirisformula" alt="f left parenthesis x right parenthesis" width="29" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»'/> when devided by <img src="data:image/png;base64,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" class="Wirisformula" alt="x to the power of 2 end exponent minus 1" width="46" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«/math»'/> is

Solution for the question - if the remainders of the polynomial f(x) when divided by x+1 and x-1 are7,3 then the remainder of f(x) when devided by x^(2)-1 is 3x+7