Question

Consider the polynomial function 𝑃(𝑥) = 2𝑥^3 − 𝑚𝑥^2 + 𝑥 − 5𝑚. The remainder when P(x) is divided by (𝑥 − 2) is four times the remainder from dividing P(x) by (𝑥 + 1). Determine m algebraically and show all your work. 

Answer 1

$Let\ P(x)=2x^3-mx^2+x-5m$

The remainder when P(x) is divided by (x-2) is;

$P(2)=2\cdot8-m\cdot4+2-5m$

$=16-4m+2-5m$

Thus: P(2)=18-9m

And the remainder when P(x) is divided by (x+1) is;

$P(-1)=-2-m-1-5m$

=-3-6m

P(-1)=-3-6m

From the question: P(2)=4*P(-1)

18-9m=4(-3-6m)

18-9m=-12-24m

-9m+24m=-12-18

15m=-30

$m=\frac{-30}{15}$

m=-2