Question

on dividing the polynomial 2x3 +4x2+5x+7 by a polynomial g(x)the quotient and remainder were 2x and 7-5x respectively find g(x)

Answer 1

g(x)=x^2+2x+5............
hope it helps.......

Answer 2

by using the division algorithem

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

2x³+4x²+5x+7=g(x) x 2x +7-5x

2x³+4x²+5x+7-7+5x=g(x) x 2x

2x³+4x²+10x / 2x=g(x)

so we should divide 2x³+4x²+10x by 2x

by long division

so g(x)=x²+2x+5