Question

On dividing x4-x 3-3x2+3x+2 by a polynomial g(x), the quotient and remainder were x2-x-2 and 2x respectively. find g(x).

Answer 1

Answer:

$g(x)=x^2-1$

Step-by-step explanation:

Concept used:

Division algorithm:

Dividend = (Divisor*quotient)+remainder

By division algorithm

$x^4-x^3-3x^2+3x+2=g(x)*(x^2-x-2)+2x$

$x^4-x^3-3x^2+x+2=g(x)*(x^2-x-2)$

$g(x)=\frac{x^4-x^3-3x^2+x+2}{x^2-x-2}$

$g(x)=\frac{x^4-x^3-2x^2-x^2+x+2}{x^2-x-2}$

$g(x)=\frac{x^2(x^2-x-2)-1(x^2-x-2)}{x^2-x-2}$

$g(x)=\frac{(x^2-1)(x^2-x-2)}{x^2-x-2}$

$g(x)=x^2-1$

Answer 2

answer is in photograph

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