# How do you factor x^2-15x+36?

Mar 19, 2018

$\left(x - 12\right) \left(x - 3\right)$

#### Explanation:

$\text{the factors of + 36 which sum to - 15 are - 12 and - 3}$

$\Rightarrow {x}^{2} - 15 x + 36 = \left(x - 12\right) \left(x - 3\right)$

Mar 19, 2018

Use middle term splitting.
${x}^{2} - 15 x + 36 = \left(x - 3\right) \left(x - 12\right)$

#### Explanation:

Spli the middle term such that the product of terms should be +36 and sum (-15).
So, check the factors of 36 which satisfies this condition.
Factors of 36 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 36
Since sum should be negative and product should be positive, both factors should be negative.
Thus the required pair of factors is -3 and -12.

${x}^{2} - 15 x + 36 = {x}^{2} - 3 x - 12 x + 36$ (Split the middle term)

$= x \left(x - 3\right) - 12 \left(x - 2\right)$
$= \left(x - 3\right) \left(x - 12\right)$