Factors and Zeros of Polynomials

Use the polynomial function $$p(x)=3x^3+11x^2+5x-3$$ to answer the question below:
1. Show whether or not $$(x+1)$$ is a factor of $$p(x)$$ using the Remainder Theorem. Explain your reasoning.
2. 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?