Let $p\left(x\right) = x^{3} – 3x^{2} – 7x + 9$.

1. Read about the Remainder Theorem in the Math Notes box in Lesson 8.3.2. Then use the Remainder Theorem to determine $p\left(5\right)$.

   Hint (a):

   $\frac{\textit{x}^3-3\textit{x}^2-7\textit{x}+9}{\textit{x}-5}=?$

2. Use the Remainder Theorem to determine $p\left(1\right)$. What does your result tell you about the polynomial?

   Hint (b):

   If there is no remainder then $\left(x − 1\right)$ is a factor.