Question

on dividing the polynomial p(x)=x³-3x²+x+2 by a polynomial g(x)the quotient q(x)nd remainder x-2 nd -2x+4 respectively. find g(x)

Answer 1

the answer is x^2-x+1

Answer 2

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] = g(x)

therefore g(x) = x²-x+1