Question

divide x^4-4x^3+8x^2+7x+10 by (x-2) and verify the division algorithm ​

Answer 1

dividend = divisor X quotient + remainder

Answer 2

Given : $x^4-4x^3+8x^2+7x+10$

Explanation:

p(x) = $x^4-4x^3+8x^2+7x+10$

g(x) = x-2

on dividing p(x) by g(x) we have

quotient = x³-2x²+4x-1

remainder = 8

verification

dividend = divisor × quotient + remainder

$x^4-4x^3+8x^2+7x+10$ =(x-2) ( x³-2x²+4x-1) +8

$x^4-4x^3+8x^2+7x+10$ = $x^4-2x^3+4x^2-x-2x^3+4x^2-8x+2 +8$

$x^4-4x^3+8x^2+7x+10$ = $x^4-4x^3+8x^2+7x+10$

hence proved

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