Question

On dividing xcube-3xsquare+x+2 by a polynomial g(x),the quotient and

remainder were x-2 and -2x+4 respectively, find g(x).​

Answer 1

Step-by-step explanation:

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

x^3-3x^2+x+2. =. g(x). (x-2). +(-2x+4)

x^3-3x^2+x+2-(-2x+4) = g(x) (x-2)

x^3-3x^2+x+2+2x+4 =. g(x) (x-2)

x^3-3x^2+x+2+2x+4/(x-2). = g(x)

x^2-x+1 =g(x)