Question

the polynomial F(x)=x^3 +3x^2 +ax+b leaves the same remainder when divided by x-2 as when divided by x+1,solve for a

Answer 1

Hi,

a=-6

Explanation:

`F(x)=x^3+3x^2+ax+b\\\\F(2)=2^3+3*2^2+a*2+b=2a+b+20= remainder\\F(-1)=(-1)^3+3*(-1)^2+a*(-1)+b=-a+b+2=the\ same\ remainder\\\\2a+b+20=-a+b+2\\\\3a=-18\\\\\boxed{a=-6}\\`