Teaching Notes 5.16: Factoring Trinomials if the Last
Term Is Negative
To factor a trinomial in the formx^2 +bx+c, students must determine the two factors of the
negative numbercwhose sum equalsb.Once they realize that this product can be found only by
multiplying a positive integer and a negative integer, they must select the correct pair of integers.- Discuss the procedures for factoring a trinomial. Students should understand that they need
to find two numbers whose product iscand whose sum isb.For example, inx^2 + 3 x−10,
c=−10 andb=3. Students must find two factors of−10 whose sum is 3. 5 and−2arethe
factors. - Emphasize that when the last term is negative, one factor will be positive and the other will
be negative. Remind your students that a product of two integers is negative when the signs
of its factors are different. - Review the information and example on the worksheet with your students. Discuss the steps
forfactoringtheexample.Besuretonotethateitheroftwopairsoffactorscouldbeused
to factor the trinomial. Emphasize that students must select two factors whose sum is 2.
Depending on their abilities, you may find it helpful to review adding integers. - Explain that not all trinomials can be factored. They can be factored only when the sum of a
pair of factors ofcis equal tob.
EXTRA HELP:
Even though the product of two integers may be negative, the sum could be positive.ANSWER KEY:
(1)(x−2)(x+3) (2)(x+4)(x−2) (3)(x−1)(x+5) (4)(x−7)(x+2)
(5)(x+8)(x−3) (6)(x−1)(x+2) (7)(x−10)(x+4) (8)(x−5)(x+6)
(9)Cannot be factored (10)(x−4)(x+3) (11)(x−8)(x+4) (12)(x+5)(x−2)
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(Challenge)Kelli is incorrect. There are six pairs of factors of−20 and she must have
overlooked two pairs. One pair of factors whose sum is−19 is−20 and 1. The polynomial can
be factored as (x−20)(x+1).
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