Question

On dividing r? - 3x² + x + 2 by a polynomial g(x), the quotient and remainder were
x-2 and -- 2x + 4, respectively. Find g(x).


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Answer 1

Answer:

Dividend =p(x)=x

3

−3x

2

+x+2

Quotient =q(x)=x−2

Remainder =r(x)=2x+4

By division algorithm, p(x)=q(x)g(x)+r(x)

⇒g(x)=

q(x)

p(x)−r(x)

⇒g(x)=

x−2

x

3

−3x

2

+x+2+2x−4

⇒g(x)=

x−2

x

3

−3x

2

+3x−2

So, g(x)=x

2

−x+1

solution

Step-by-step explanation:

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