Think of the process as multiplying two binomials in reverse.
Prime
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^2-11x+15
In this case, we have 15. 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 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^2-11x+15
For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, - 11.
Factor Constants
Product of Constants and Variables
Sum of Products
1 and 15
1x and 15x
16x
- 1 and - 15
- 1x and - 15x
- 16x
3 and 5
3x and 5x
8x
- 3 and - 5
- 3x and - 5x
- 8x
We did not find a factor constants whose product is 15 and also cause the sum of the products of x and the factor constants to equal - 11x. Thus, the polynomial is not factorable.
