Question

On dividing ×^4 -x^3-3x^2+3x+2 by polynomial g(x) the quotient and the remainder are x^2-x-2 & 2x respectively find g(x)

Answer 1

Your answer is in the attachment below.

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Answer 2

$\boxed{QUESTION:-}$

On dividing ×^4 -x^3-3x^2+3x+2 by polynomial g(x) the quotient and the remainder are x^2-x-2 & 2x respectively find g(x)?

$\boxed{SOLUTION:-}$

p(x)=x⁴-x³-3x²+3x+2

g(x)=?

q(x)=x²-x-2

r(x)=2x

We know,

p(x)=g(x)×q(x)+r(x)

Puting the Values,

x⁴-x³-3x²+3x+2=g(x)×(x²-x-2)+2x

x⁴-x³-3x²+3x-2x+2=g(x)×(x²-x-2)

=>$\frac{\cancel {x^4-x^3-3x^2+x+2}}{\cancel {x^2-x-2}}$ =x²-1[For Division check Attachment!]

=>x²-1=g(x)

$\mathcal{BE \: BRAINLY}$