Start by identifying a, b, and c. What are the given values? What is the missing value?
Example Values: 34 and 29 Example Factored Expressions: (n+1)(6n+28) and (3n+4)(2n+7)
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.
6n^2+ n+28 ⇔ 6n^2+ b n+ 28We have that a= 6 and c= 28. Next, we need to find the product of a and c.
6 * 28=168
Now, we will find two ways of writing 168 as a product of two factors. Two possible values for b are the sum of those factors.
Written as a Product
Factors
b
168=6 * 28
6 and 28
6+28= 34
168=8 * 21
8 and 21
8+21= 29
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.
