Question

if \\((x + 4)\\) is a factor of polynomial \\(p\\), which statement must be true? \\(\bigcirc\\) a. \\(p(4) < 0\\) \\(\bigcirc\\) b. \\(p(-4) > 0\\) \\(\bigcirc\\) c. \\(p(-4) = 0\\)

Explanation:

Step1: Recall the 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 the given factor

In the problem, the factor is \((x + 4)\), which can be rewritten as \((x - (-4))\).

Step3: Apply the Factor Theorem

Using the Factor Theorem, if \((x - (-4))=(x + 4)\) is a factor of \(p(x)\), then \(p(-4)=0\).

Answer:

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