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.
"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
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