Question

for an unknown polynomial function $p(x)$, $p(4) + 2 = 2$. which binomial is a factor of $p(x)$? a $x - 2$ b $x + 2$ c $x - 4$ d $x + 4$

Explanation:

Step1: Simplify the given equation

We start with the equation \( p(4) + 2 = 2 \). Subtract 2 from both sides of the equation:
\( p(4) + 2 - 2 = 2 - 2 \)
\( p(4)=0 \)

Step2: Apply the Factor Theorem

The Factor Theorem states that if \( p(a) = 0 \), then \( (x - a) \) is a factor of the polynomial \( p(x) \). Here, we found that \( p(4)=0 \), so by the Factor Theorem, \( (x - 4) \) is a factor of \( p(x) \).

Answer:

C. \( x - 4 \)