Is there a greatest common factor between all of the terms in the given expression? If so, you should factor that out first.
(x-5)(x+15)
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.
x^2+10x - 75
In this case, we have -75. This is a negative number, so for the product of the constant terms in the factors to be negative, these constants must have the opposite sign (one positive and one negative).
Constants
Product of Constants
1 and -75 or -1 and 75
-75
3 and -25 or -3 and 25
-75
5 and -15 or -5 and 15
-75
Next, let's consider the coefficient of the linear term.
x^2+ 10x - 75
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, 10.
Constants
Sum of Constants
1 and -75
-74
-1 and 75
74
3 and -25
-22
-3 and 25
-22
5 and -15
-10
-5 and 15
10
We found the factors whose product is -75 and whose sum is 10.
x^2+ 10x - 75 ⇔ (x-5)(x+15)
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!
