Question

select the correct answer.
if ((x + 4)) is a factor of polynomial (p), which statement must be true?
a. (p(4)=0)
b. (p(-4)=0)
c. (p(4)<0)
d. (p(-4)>0)

Explanation:

Step1: Apply Factor Theorem

If $(x + a)$ is a factor of polynomial $p(x)$, then $p(-a) = 0$. Here, the factor is $(x + 4)$, so $a=4$.

Step2: Evaluate the polynomial

Substitute $x=-4$ into the polynomial condition: $p(-4) = 0$.

Answer:

B. $p(-4) = 0$