Question

4. On dividing x³- 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

Step-by-step explanation:

p(x)=g(x)q(x)+r(x)

x³- 3x²+x+ 2=g(x)(x-2)+(-2x + 4)

x³- 3x²+x+ 2+2x-4=g(x)(x-2)

x³-3x²+3x-2/(x-2)=2=g(x)

x-2)x³ -3x²+3x-2(x²-x+1

(-)x³(+)-2x²

-x² +3x

(+)-x²(-)2x

x -2

(-)x(+)-2

0

Therefore, g(x)=x²-x+1.