Start by identifying a, b, and c. What are the given values? What is the missing value?
Example Values: - 34 and - 50 Example Factored Expressions: (r+1)(8r-42) and (r-7)(8r+6)
Practice makes perfect
First, we will find two different values that complete the expression so that the trinomial can be factored into the product of two binomials. Then we will factor the resulting trinomials.
Finding Two Different Values
Let's start by identifying the given and missing coefficients in the quadratic expression.
8r^2+ r-42 ⇔ 8r^2+ b r+( - 42)We have that a= 8 and c= - 42. Next, we need to find the product of a and c.
8 ( - 42)=- 336
Now, we will find two ways of writing - 336 as a product of two factors. Two possible values for b are the sum of those factors.
Written as a Product
Factors
b
- 336=8 * (- 42)
8 and - 42
8+(- 42)= - 34
- 336=6 * (- 56)
6 and - 56
6+(- 56)= - 50
Note that there are several possible missing values, these are only two options.
Factoring the First Trinomial
We will assume that b= - 34 and factor the quadratic expression.
