Consider the equation $5x^{2} − 7x − 6 = 0$ as you answer the questions in parts (a) through (d) below.

1. What are the factors of $5x^{2} − 7x − 6$?

   Answer (a):

   $\left(5x + 3\right)\left(x − 2\right)$

2. What are the solutions to the equation?

   Hint (b):

   Use the factors to find the values.

   Answer (b):

   $\textit{x}=2,\,-\frac{3}{5}$

3. Explain the relationship between the factors of the polynomial expression and the solutions to the equation.

   Answer (c):

   The relationship is that the solutions are the numbers that would make the factors equal to $0$.

4. How are the solutions to the equation related to the lead coefficient and constant term in the original polynomial?

   Answer (d):

   $3$ and $2$ are factors of $6$ while $5$ is a factor of the lead coefficient.