# How do you factor the expression 6x^2 - 27x - 15?

May 8, 2018

$3 \left(x - 5\right) \left(2 x + 1\right)$

#### Explanation:

$6 {x}^{2} - 27 x - 15 = 6 {x}^{2} - 30 x + 3 x - 15$

$= 6 x \left(x - 5\right) + 3 \left(x - 5\right) = \left(x - 5\right) \left(6 x + 3\right)$

$3 \left(x - 5\right) \left(2 x + 1\right)$ [Ans]

May 8, 2018

$\left(3 x - 15\right) \left(2 x + 1\right)$

#### Explanation:

First, we need to find which two numbers multiply with each other to give -90 (-15xx6)and when added together it gives $- 27$.

So lets find the multiples of -90:
$- 2 \times 45$
$- 6 \times 15$
$- 30 x 3$-----> this when multiplied gives $- 90$ and adding gives us $- 27$.

$6 {x}^{2} - 27 x - 15$
$6 {x}^{2} + 3 x - 30 x - 15$
$3 x \left(2 x + 1\right) - 15 \left(2 x + 1\right)$
$\left(3 x - 15\right) \left(2 x + 1\right)$