# Is it possible to factor y=x^2+15x+36 ? If so, what are the factors?

May 16, 2018

Factoring $y = {x}^{2} + 15 x + 36$ gives us $\left(x + 3\right) \left(x + 12\right)$

#### Explanation:

So to factor $y = \left({x}^{2} + 15 x + 36\right)$, we need to find values that give us the middle term as we know that x times x gives us ${x}^{2}$ so that they be in both binomial. So let think of factors that gives us 36 but add up to 15.

6 x 6 = 36 | 6 + 6 = 12 - This set of numbers do not work
18 x 2 = 36 | 18 + 2 = 20 - This set of numbers do not work
12 x 3 = 36 | 12 + 3 = 15 - This set of numbers do work.

So we now can plug in numbers and since $y = {x}^{2} + 15 x + 36$ has positive values, we do not need to worry about if a number need to have a negative sign or not.

So factoring $y = {x}^{2} + 15 x + 36$ gives us $\left(x + 3\right) \left(x + 12\right)$