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+9x+18
In this case, we have 18. 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 signs - both positive or both negative.
Factor Constants
Product of Constants
1 and 18
18
-1 and -18
18
2 and 9
18
-2 and - 9
18
3 and 6
18
-3 and - 6
18
Next, let's consider the coefficient of the linear term.
x^2+9x+18
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, 9.
Factors
Sum of Factors
1 and 18
19
-1 and -18
- 18
2 and 9
11
-2 and - 9
- 11
3 and 6
9
-3 and - 6
- 9
We found the factors whose product is 18 and whose sum is 9.
x^2+9x+18 ⇔ (x+3)(x+6)
Checking Our Answer
Check your answer âś“
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!
