Question

Use synthetic division to find p where f(x) = 2x ^ 3 + 5x ^ 2 + px + 8 and f(- 2) = 10

Answer 1

Given:

$\begin{gathered} f(x)=2x^3+5x^2+px+8 \\ f(-2)=10 \end{gathered}$

We're going to find the value of p:

$\begin{gathered} f(-2)=2(-2)^3+5(-2)^2+p(-2)+8 \\ f(-2)=2(-8)+5(4)-2p+8 \\ f(-2)=-16+20-2p+8 \\ f(-2)=-2p+12 \end{gathered}$

Given that f(-2)=10, we could equal:

$\begin{gathered} -2p+12=10 \\ -2p=10-12 \\ -2p=-2 \\ p=1 \end{gathered}$

Therefore, p=1.