Think of the process as multiplying two binomials in reverse.
(x+8)(x+5)
Practice makes perfect
To factor a trinomial with a leading coefficient of one, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term.
x^2+13x+40
In this case, we have 40. 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.) Let's also consider the coefficient of the linear term.
x^2+13x+40
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, 13. Since a sum of two negative numbers is never positive, we should only consider positive constants.
Constants
Product of Constants
Sum of Constants
1 and 40
40
41
2 and 20
40
22
4 and 10
40
14
5 and 8
40
13
Now we can write the products of the constants and variables.
5x and 8x
We found the factor constants whose product is 40 and also cause the sum of the products of x and the factor constants to equal 13x.
x^2+13x+40 ⇔ (x+5)(x+8)
or
x^2+13x+40 ⇔ (x+8)(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!
