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^2-2x-15
In this case, we have - 15. This is a negative number, so for the product of the constant terms in the factors to be negative, these constants must have different signs - positive or negative.
Factor Constants
Product of Constants
1 and - 15
- 15
-1 and 15
- 15
3 and - 5
- 15
-3 and 5
- 15
Next, let's consider the coefficient of the linear term.
x^2- 2x-15
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, - 2.
Factors
Sum of Factors
1 and - 15
- 14
-1 and 15
14
3 and - 5
- 2
-3 and 5
2
We found the factors whose product is - 2 and whose sum is - 15.
x^2- 2x-15 ⇔ (x+3)(x-5)
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!
