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.
x^2+7x+ 12
In this case, we have 12. 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 12
12
-1 and -12
12
2 and 6
12
-2 and -6
12
3 and 4
12
-3 and -4
12
Next, let's consider the coefficient of the linear term.
x^2+ 7x+ 12
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, 7.
Factors
Sum of Factors
1 and 12
13
-1 and -12
-13
2 and 6
8
-2 and -6
-8
3 and 4
7
-3 and -4
-7
We found the factors whose product is 12 and whose sum is 7.
x^2+ 7x+ 12 ⇔ (x+4)(x+3)
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!
