### Home > A2C > Chapter 9 > Lesson 9.3.1 > Problem9-126

9-126.

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 $5x^{2} − 7x − 6$?

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

2. What are the solutions to the equation?

Use the factors to find the values.

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

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

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?

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