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

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.

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 = -14 -14 + 1 = -13 👎 -7 x 2 = -14 -7 + 2 = -5 👍

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 + 70. 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 = -70 70 + -1 = 69 👎 35 x -2 = -70 35 + -2 = 33 👎 14 x -5 = -70 14 + -5 = 9 👎 10 x -7 = -70 10 + -7 = 3 👍