# How do you factor 3x^2 - 5x - 12?

Aug 4, 2017

The answer is $\left(x - 3\right) \left(3 x + 4\right)$.

#### Explanation:

![https://d2jmvrsizmvf4x.cloudfront.net/uA9v8owQVa0rRLtH5qXG_1501845782432413515707.jpg)

Aug 4, 2017

3x^2−5x−12

$= \left(x - 3\right) \left(3 x + 4\right)$

#### Explanation:

Another Method
$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$a = 3$
$b = - 5$
$c = - 12$

Applying Formula we get,

(-(-5)+-sqrt(-5^2-4(3)(-12)))/(2(3)
$\frac{+ 5 \pm \sqrt{25 + 144}}{6}$
$\frac{5 \pm \sqrt{169}}{6}$

$\frac{5 \pm \left(13\right)}{6}$

$x = \frac{5 + 13}{6} = \frac{18}{6} = 3$ _ here $\left(x - 3\right)$
and
$x = \frac{5 - 13}{6} = - \frac{8}{6} = - \frac{4}{3}$ _ here $\left(3 x + 4\right)$

Aug 4, 2017

$\left(x - 3\right) \left(3 x + 4\right)$

#### Explanation:

$3 {x}^{2} - 5 x - 12$ is a quadratic trinomial.

Find factors of $3 \mathmr{and} 12$ whose products differ by $5$

$\text{ "3 " & } 12$
$\text{ "darr" } \downarrow$

$\text{ "1" "3" } \rightarrow 3 \times 3 = 9$
$\text{ "3" "4" } \rightarrow 1 \times 4 = \underline{4}$
$\textcolor{w h i t e}{w . w w w w w w w w w w . . w w w w} 5$

We have correct factors, now fill in the signs to get$- 5 \mathmr{and} 12$

$\text{ "1" "-3" } \rightarrow 3 \times - 3 = - 9$
$\text{ "3" "+4" } \rightarrow 1 \times + 4 = + \underline{4}$
$\textcolor{w h i t e}{w . w w w w w w w w w w w w w w . w w w w} - 5$

$3 {x}^{2} - 5 x - 12$

$= \left(x - 3\right) \left(3 x + 4\right)$