# How do you factor 3x^2 + 45x + 162?

Jun 7, 2016

$\left(3 x + 27\right) \left(x + 6\right)$

#### Explanation:

Find factors of 3 and 162 which ADD to 45.
45 is quite small compared to 162. This is an indication that we will need small factors of 162.

There are a few options which come to mind:
54 x 3 (54 is already too big)
27 x 6 is possible
18 x 9 is possible

The chosen factors have to be combined with 3 x 1 to give a sum of 45.

27 x 3 is too big
18 x 3 is too big

3 x 6 + 1 x 27 = 18 = 27 = 45. BINGO!

$\left(3 x + 27\right) \left(x + 6\right)$ will give us the combination we need.