Question

f(x) is a polynomial equation. If you divide f(x) by 2x+1, the remainder is 4 and when we call dividend q(x), q(x) is multiple of x-1. What is g(1) if g(x) is the dividend of (x^2+x+1)f(x) divided by x+(1/2)?

Answer 1

f(-1/2)=(2x+1)(qx)+4
(x^2+x+1)f(x)/x+1/2=q(x)
f(x)=q(x)(x+1/2)/x^2+x+1
f(-1/2)=q(x)(-1/2+1/2)/1/4-1/2+1
f(-1/2)=0
q(x)(2x+1)+4=0
q(x)=-4/2x+1