1. More practice with trinomial factoring Exceptional Cases
Unit 14: Lesson 3
More practice with trinomial factoring
Exceptional Cases

2. Consider factoring a trinomial
Consider factoring a trinomial. Before applying the box method, factor out a GCF.
Before applying the box method of factoring a trinomial, some “pre-factoring must be done if either of the following is true:
A GCF can be factored out of the trinomial (see Example 1 on the next slide).
First, factor out the GCF and then apply the box method.
The coefficient of the squared term is negative (see Example 2).
First, factor out -1 and then apply the box method.

3. Example 1: Use the box method to find the factors of 4x2 – 10x – 14
Example 1: Use the box method to find the factors of 4x2 – 10x – 14. Specify the product and sum that were used in arriving at the answer.
The GCF of 4, 10, and 14 is 2.
Thus, 4x2 – 10x - 14 = 2(2x2 – 5x - 7) x 1
2x2 -7
Answer: 4x2 – 10x -14 = 2(2x – 7)(x + 1) 2x -7
-7x 2x
Product: (2x2)(-7) = -14x2
Sum: -10x (middle term of trinomial)
-14 x 1 = = -13 👎
-7 x 2 = = -5 👍

4. Example 2: Use the box method to find the factors of -p2 – 3p + 70
Example 2: Use the box method to find the factors of p2 – 3p Specify the product and sum that were used in arriving at the answer.
Factor out a -1. Thus, -p2 – 3p + 70 = -(p2 + 3p - 70) p 10 p2
-70
Answer: 4x2 – 10x -14 = 2(2x – 7)(x + 1) p -7
-7p
10p
Product: (p2)(-70) = -70p2
Sum: 3p (middle term of trinomial)
70 x -1 = = 69 👎
35 x -2 = = 33 👎
14 x -5 = = 9 👎
10 x -7 = = 👍