Question

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

Explanation:

Step1: Analyze the given equation

We know that \( p(4)+2 = 2 \). Subtract 2 from both sides: \( p(4)=2 - 2=0 \).

Step2: Recall the Factor Theorem

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

Answer:

A. \( x - 4 \)