Question
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 9 minus 8](data:image/png;base64,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)
The correct answer is: Thus, the simplified expression is; x^9 - 8 = (x^3 - 2) (x^6+2x^3+4)
ANSWER:
Hint:
, here a and b can be real values, variables or multiples of both.
We are asked to use polynomial identities to factorize the given expression.
Step 1 of 2:
The given expression is
. ![text Ne can rewrite it as, end text x to the power of 9 minus 8 equals open parentheses x cubed close parentheses cubed minus left parenthesis 2 right parenthesis cubed text . It is of the form end text open parentheses a cubed minus b cubed close parentheses text . end text](data:image/png;base64,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)
![text Here, end text a equals x cubed straight & b equals 2 text . end text](data:image/png;base64,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)
Step 2 of 2:
Use the polynomial identity to simplify the expression;
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x to the power of 9 minus 8 equals open parentheses x cubed close parentheses cubed minus left parenthesis 2 right parenthesis to the power of 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end exponent end cell row cell equals open parentheses x cubed minus 2 close parentheses open parentheses open parentheses x cubed close parentheses squared plus open parentheses x cubed close parentheses left parenthesis 2 right parenthesis plus open parentheses 2 squared close parentheses close parentheses space space space space space space end cell row cell equals open parentheses x cubed minus 2 close parentheses open parentheses x to the power of 6 plus 2 x cubed plus 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space end cell end table space space space space space space space space space space space space](data:image/png;base64,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)
Thus, the simplified expression is;
.
Note:
Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.
Related Questions to study
Use Pascal triangle to expand![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
Use Pascal triangle to expand![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
Use binomial theorem to expand (x - 3)4
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use binomial theorem to expand (x - 3)4
For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 8 minus 9](data:image/png;base64,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)
Use polynomial identities to factor the polynomials or simplify the expressions :
![x to the power of 8 minus 9](data:image/png;base64,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)
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,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)
How is
obtained from ![left parenthesis x plus y right parenthesis to the power of n minus 1 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAASCAYAAADxEzisAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAeFJREFUeNpjYBgFuIAaENcC8QV8irKAuGOQeqAD6j56gcVAnAbE/3Ep0APi44M81o9C3YkObgCxDxCfAeJfQFxORTv/43OMwSAPMGMgPowmxgTEf6ApQhrqh3e0DjADaIANBXAYGnAwYA5NWTBgDcR7cXgcFyY5wLqAOIdGHvxPZfPy0MrZSCBeiMafT2v37wBiWyziyTgqgWaoHDUDbC4Qh2MRLwDiViS+JVoKmgTEGWj8ZFoH2CcgZsOh4RwQiyPxE4F4Cg1SWDw0pSMDLiC+BcTCSGJsUPfCwDog9kLib0Dj0yTA/uDR4AHEfVC2C47ygRoBBvLkKjSxemhbCB38QmKDCngOPHxKAgpnWfeHgObdQGwPbcQJk2ERMYUsyNwrSHxRIL6Lw/O/BrrmwZclYeXILxxtIGoW+t+Q2H1Qe9EBepYcELAbWh1jAyDxNVAPRNI4wEBNBiUovgttY6EDSzKKBaoDXM0KkMM3QQtfHmh7R5iGAQZqHvgB8VIgjsWhJgdL5UB3gK3hCipDtqEFkA+0RU2rACuANi8ukdBwHTBwHKmMYoNW19JY1C2H1py0AAHQAPYjoWs0YGAwdL79CLjhKJkVD81AxgAP72yDFuq4ytk0hlEABzpAvGWwOxIAhE5455JPXB8AAACwdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPig8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPnk8L21pPjxtc3VwPjxtbz4pPC9tbz48bXJvdz48bWk+bjwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1cD48L21hdGg+8mttWgAAAABJRU5ErkJggg==)
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use Pascal triangle to expand (x + y)6
The expansion of the polynomial (x + y)6 can be found using the values of 6Cr
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 25 straight x squared minus 15 straight y squared close parentheses open parentheses 25 straight x squared plus 15 straight y squared close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![12 cubed plus 2 cubed](data:image/png;base64,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)
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The answer cam also be found by expanding the formula of 5Cr .
Use Pascal triangle to expand ![left parenthesis x plus y right parenthesis to the power of 5](data:image/png;base64,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)
The answer cam also be found by expanding the formula of 5Cr .
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![open parentheses 3 x squared minus 4 x y close parentheses open parentheses 3 x squared plus 4 x y close parentheses](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![27 x to the power of 9 minus 343 y to the power of 6](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 10 plus 21 right parenthesis squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAARCAYAAACVW1F7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAPUJuPDwAAAc9JREFUeNpjYBgF6OA/FP8C4qNArIJLYRYQd4yQQOmA+hcXYILKn8MmqQfEx0dYKjoK9Tc+8AOXRgMs4mpAXAvEF/AYyAfE04D4JBTPhIpRG1gD8Rog/gTNJiA3ReNRT8jtxkB8GI9+eyA+iC5oAA0sbGAxEKdB8zEusBeI/ZD4PlAxagOQwyOBmAfK14K6O5ICtx+GBho6kISarYQu0QXEOUQUfNhAKBBPwiI+AY8niDWbGCAPxJcoMD8PSzkNSpFboAGGAXYAsS2ZFoKyhRsWcUeoHK0DC2e5QqT5lmi5ABRA2/AVI6AygI1MC9/h0AsSe0mHwLLEU4QQYz4b1P8wAAooDXyG/aHAQ/j0/qJxYHFAKxRrCs3/haWdhYzpElg/CDT88GFCQBCIN+AoAigJLIKAkmz4EodeDhpmQyVoQKlQwXz0bEgQ7KYgKYMKcQ8s4m40KuBB5clsIOYisQtDbAFPEFDSdAiCOh4dzKdB00EciFcBMQsZ/T1cIAfqf6KBAYU1yn4gLoB6ApSsq7G1fKkQWFsI1VRkmI+rUYoXHMfRTyKm8AUVtnOhBfo3aHeHh4YjAsRWCITUEeru4ASjHWkSQcYIGqLpgvYbiQYAVpSR0gG65vMAAACKdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPig8L21vPjxtbj4xMDwvbW4+PG1vPis8L21vPjxtbj4yMTwvbW4+PG1zdXA+PG1vPik8L21vPjxtbj4yPC9tbj48L21zdXA+PC9tYXRoPk4xinAAAAAASUVORK5CYII=)
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How is ( x + y )n obtained from (x + y)n-1
You could also get the value of from
by just multiplying a ( x + y) with
.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ?
![m to the power of 8 minus 9 n to the power of 10](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
Use polynomial identities to multiply the expressions ?
![left parenthesis 7 plus 9 right parenthesis squared](data:image/png;base64,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)
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.
How can you use polynomial identities to factor polynomials and simplify numerical expressions ? 123 + 23
This can also be done by finding the cube of each values and adding them. But that might be time consuming. Hence, we use these identities.