Question

3
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: Recall Factor Theorem

The Factor Theorem states that if \((x - a)\) is a factor of a polynomial \(p(x)\), then \(p(a)=0\).

Step2: Adjust for Given Factor

In the problem, the factor is \((x + 4)\), which can be rewritten as \((x-(-4))\). Comparing with \((x - a)\), we have \(a=-4\).

Step3: Apply Factor Theorem

By the Factor Theorem, since \((x + 4)=(x-(-4))\) is a factor of \(p(x)\), we must have \(p(-4) = 0\).

Answer:

B. \( p(-4) = 0 \)