# How do you factor the trinomial 3x^2 + 12x + 7 ?

##### 1 Answer
Nov 21, 2015

To factor the trinomial, we use the quadratic formula to solve for the zeros, which are $\frac{- 6 \pm \sqrt{15}}{3}$ or $- 0.71$ and $- 3.29$.

#### Explanation:

Since there is no common factor between any of the three terms, we have to use the quadratic formula:

$a = 3$
$b = 12$
$c = 7$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{- \left(12\right) \pm \sqrt{{\left(12\right)}^{2} - 4 \left(3\right) \left(7\right)}}{2 \left(3\right)}$

$x = \frac{- 12 \pm \sqrt{\left(144\right) - \left(84\right)}}{6}$

$x = \frac{- 12 \pm \sqrt{60}}{6}$

$x = \frac{- 12 \pm 2 \sqrt{15}}{6}$

$x = \frac{2 \left(- 6 \pm 1 \sqrt{15}\right)}{2 \left(3\right)}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(- 6 \pm 1 \sqrt{15}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(3\right)}$

$x = \frac{- 6 \pm \sqrt{15}}{3}$

$x = - 0.71$ or $- 3.29$

If your answer is supposed to be exact, your answer is:

$x = \frac{- 6 \pm \sqrt{15}}{3}$

Otherwise, you can continue to solve for the approximate values of $x$.