# How do you factor the expression 9x^2+9x+2?

Dec 24, 2015

You look for its roots with the quadratic formula.

#### Explanation:

We first need $\Delta = {b}^{2} - 4 a c = 9$. So there are two real roots.

By the quadratic formula, a root is given by the expression $\frac{- b \pm \sqrt{\Delta}}{2} a$. We apply it here.

${x}_{1} = \frac{- 9 - 3}{18} = - \frac{2}{3}$ and ${x}_{2} = \frac{- 9 + 3}{18} = - \frac{1}{3}$.

So this polynomial is equal to $9 \left(x + \frac{2}{3}\right) \left(x + \frac{1}{3}\right)$.