Is there a greatest common factor between all of the terms in the given expression? If so, you should factor that out first.
(z+3)(z+12)
Practice makes perfect
To factor a trinomial with a leading coefficient of 1, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term.
z^2+15z+36
In this case, we have 36. This is a positive number, so for the product of the constant terms in the factors to be positive, these constants must have the same sign (both positive or both negative.)
Factor Constants
Product of Constants
1 and 36
36
-1 and -36
36
2 and 18
36
-2 and -18
36
3 and 12
36
-3 and -12
36
4 and 9
36
-4 and -9
36
6 and 6
36
-6 and -6
36
Next, let's consider the coefficient of the linear term.
z^2+15z+36
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, 15.
Factors
Sum of Factors
1 and 36
37
-1 and -36
-37
2 and 18
20
-2 and -18
-20
3 and 12
15
-3 and -12
-15
4 and 9
13
-4 and -9
-13
6 and 6
12
-6 and -6
-12
We found the factors whose product is 36 and whose sum is 15.
z^2+15z+36 ⇔ (z+3)(z+12)
Checking Our Answer
Check your answer ✓
We can check our answer by applying the Distributive Property and comparing the result with the given expression.
After applying the Distributive Property and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!
