# Factors and Zeros of Polynomials

Performance Task

Use the polynomial function \(p(x)=3x^3+11x^2+5x-3\) to answer the question below:

- Show whether or not \((x+1)\) is a factor of \(p(x)\) using the Remainder Theorem. Explain your reasoning.
- In the process of solving \(2x^3+7x^2+9x+10=0\) you test 1, 2, 5, and 10 as possible zeros and determine that none of them are actual zeros. You then discover that \(-\dfrac{5}{2}\) is a zero.

After using synthetic division, the quotient is \(2x^2+2x+4\). Do you need to test 1, 2, 5, and 10 again? Why or why not?