Question

On dividing x3 - 3x2 + x + 2 by a polynomial g(x), the quotient and remainder are x-2 and 4-2x respectively. Find g(x).​

Answer 1

Answer:

dividend =x³-3x²+x+2

divisor=g(x)

quotient =x-2

remainder =4-2x

dividend =divisor ×quotient +remainder

x³-3x²+x+2=g(x)×(x-2)+4-2x

x³-3x²+x+2-4+2x=g(x)×(x-2)

x³-3x²+3x-2=g(x)×(x-2)

x³-3x²+3x-2÷x-2=g(x)

x²-x+1=g(x)