Maths-
General
Easy

Question

If the remainders of the polynomial f left parenthesis x right parenthesis when divided by x plus 1 and x minus 1 are 7,3 then the remainder of f left parenthesis x right parenthesis when devided by x to the power of 2 end exponent minus 1 is

  1. 3x+5    
  2. 2x+7    
  3. -2x+5    
  4. 3x+7    

Hint:

Dividend = Divisor cross times Quotient + remainder
f(x) = g(x) cross times q(x) + r(x)

The correct answer is: -2x+5


    Dividend = Divisor cross times Quotient + remainder
    f(x) = g(x) cross times q(x) + r(x)
    f(x) = (x+1)cross times  q1(x) + 7
    f(-1) = 7
    f(x) = (x-1) cross times q2(x) + 3
    f(1) = 3
    f(x) is divided with x squared space minus 1
    Let remainder be ax + b and quotient  be q3(x)
    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

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