Question

1. the remainder theorem states that the remainder from p(x) divided by (x - a) is equal to p(a). therefore, if p(a)=0, the remainder is 0, which means that (x - a) is a factor of p(x). consider a polynomial p(x), such that p(-8)=3, p(-4)=0, p(4)=1, and p(0)=-8. use the remainder theorem to determine which of these is a factor of p(x). a. (x + 8) b. (x + 4) c. (x - 4) d. (x + 0)

Explanation:

Step1: Recall remainder - theorem condition

According to the remainder theorem, if \(p(a)=0\), then \((x - a)\) is a factor of \(p(x)\).

Step2: Check each option

We are given \(p(-8)=3\), \(p(-4) = 0\), \(p(4)=1\) and \(p(0)=-8\). For \((x + 8)\), \(a=-8\) and \(p(-8)
eq0\). For \((x + 4)\), \(a=-4\) and \(p(-4)=0\). For \((x - 4)\), \(a = 4\) and \(p(4)
eq0\). For \((x+0)\) (i.e., \(x\)), \(a = 0\) and \(p(0)
eq0\).

Answer:

B. \((x + 4)\)