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On dividing (x^(2)-3x^(2)+x+2) by a poly...

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

A

`x^2-x+3`

B

`x^2-x+1`

C

`x^2-x+2`

D

`x^2-x`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `" "p(x)=x^(3)-3x^(2)+x+2`,
`q(x)=x-2 and r(x)=-2x+4` then, `" " p(x)=q(x)xxg(x)+r(x)`
`implies q(x)xxg(x)=p(x)-r(x)=(x^(3)-3x^(2)+x+2)-(-2x+4)`
`=x^(3)-3x^(2)+x+2+2x-4=x^(3)-3x^(2)+3x-2`
`implies " " g(x)=(x^(3)-3x^(2)+3x-2)/(x-2)`
Now, dividing `x^(3)-3x^(2)+3x-2` by x-2, we get g(x),

`:. " " g(x)=x^(2)-x+1 " "` Ans.
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