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

$\text{Since x-2 and x+1 divides P(x), we have that at x = 2 and x = -1, therefore}\\ 2(2)^3-m(2)^2+2-5m = R(x)\\ 2(-1)^3 - m (-1)^2+ 2 -5m=R(x)\\ \text{Therefore, we have }\\ 18-9m= -12-24m\\ 15m=-30\\ \implies m = -2$