Question

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

Answer 1

Given the function f(x):

$f(x)=2x^3+5x^2+px+8$

And f(-2) = 10

So, we will substitute with x = -2

$2(-2)^3+5(-2)^2+p(-2)+8=10$

solve the equation to find p

$\begin{gathered} 2(-8)+5(4)-2p+8=10 \\ -16+20-2p+8=10 \\ -2p+12=10 \\ -2p=10-12 \\ -2p=-2 \\ p=\frac{-2}{-2}=1 \end{gathered}$

So, the answer will be the first option p = 1