# How do you factor 36a^2-3a-5?

May 5, 2016

 color(blue)((3a + 1) (12a - 5)  is the factorised form of the expression.

#### Explanation:

$36 {a}^{2} - 3 a - 5$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $x {a}^{2} + y a + z$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = x \cdot z = 36 \cdot \left(- 5\right) = - 180$

AND

${N}_{1} + {N}_{2} = b = - 3$

After trying out a few numbers we get ${N}_{1} = - 15$ and ${N}_{2} = 12$

$12 \cdot \left(- 15\right) = - 180$, and $12 + \left(- 15\right) = - 3$

$36 {a}^{2} - 3 a - 5 = 36 {a}^{2} - 15 a + 12 a - 5$

$= 3 a \left(12 a - 5\right) + 1 \left(12 a - 5\right)$

 = color(blue)((3a + 1) (12a - 5)