# Is it possible to factor #y=x^2 + 12x + 36 #? If so, what are the factors?

##### 1 Answer

Yes;

#### Explanation:

There are multiple ways to factor trinomials, so let's begin by asking:

*What two numbers multiply to give 36 and add to give 12?*

There are only a handful of numbers that multiply to give 36, so the guess and check methods isn't a bad idea. Let's write the possible factors of 36 and find their sum:

Looks like we found a pair! So, the factorization becomes:

Another way to do this is knowing a special case of trinomials called perfect square trinomials. All trinomials that are a perfect square of a binomial are of the form:

In this case,

We can also double check our answer by comparing the graphs:

graph{x^2+12x+36 [-10, 10, -5, 5]}

graph{(x+6)^2 [-10, 10, -5, 5]}

They are identical, confirming we have found the right answer.