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Unit 14: Lesson 3. More practice with trinomial factoring Exceptional Cases. 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:
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Unit 14: Lesson 3 More practice with trinomial factoring Exceptional Cases
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. 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) 1 x 2x 2x2 2x Answer: 4x2 – 10x -14 = 2(2x – 7)(x + 1) -7 -7x -7 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. Specify the product and sum that were used in arriving at the answer. • Factor out a -1. Thus, -p2 – 3p + 70 = -(p2+ 3p - 70) 10 p Answer: 4x2 – 10x -14 = 2(2x – 7)(x + 1) p p2 10p -70 -7p -7 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 👍
