Question

On dividing x^3- 3x^2 + x + 2 by a polynomial g(x), the quotient and remainder were x- 2 and - 2x+4 respectively.Find g(x)?

Answer 1

$x^3-3x^2+x+2$ is the dividend.

Let the dividend be P(x), P(x) means; polynomial for x.

Then we have $P(x)=g(x)(x-2)-2x+4$.

By moving the side of the remainder, we get $g(x)(x-2)=P(x)+2x-4$.

We can rewrite $P(x)=x^3-3x^2+x+2$.

Now we have $g(x)(x-2)=x^3-3x^2+3x-2$.

By dividing both sides by x-2, we get x²-x+1. Therefore g(x)=x²-x+1.

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