Teaching Notes 5.15: Factoring Trinomials if the Last Term
Is Positive
Factoring a trinomial means to write the trinomial as the product of its factors. To factor a
trinomial in the formx^2 +bx+c, you must find two factors ofcwhose sum equalsb. Becausecis
a positive term, it is necessary to understand that the factors ofcmust both be positive or both
be negative. Students often forget this fact, which leads to mistakes.- Explain that a trinomial may be the product of two binomials. For example,x^2 + 5 x+4isthe
product of (x+4) and (x+1). When students factor a trinomial, they must find two binomi-
als whose product is equal to the trinomial. If the last term,c, of the trinomial is a positive
integer, finding the factors ofcis necessary to factor the trinomial. (cmay be negative but
that will be discussed in 5.16: ‘‘Factoring Trinomials if the Last Term Is Negative.’’) - Review the information and example on the worksheet with your students, particularly the
steps for factoring trinomials. When discussing the examples, emphasize that when the last
term is positive, the factors are a pair of positive numbers or a pair of negative numbers. The
sign of the second term,b, indicates whether the pair is positive or negative. - Point out that not all trinomials can be factored. They may be factored only when the sum of
a pair of factors ofcis equal tob.
EXTRA HELP:
Whenbis positive, the factors ofcwill also be positive. Whenbis negative, the factors ofcwill be
negative.ANSWER KEY:
(1)(x+1)(x+5) (2)(x+2)(x+4) (3)(x−3(x−2) (4)(x−4)(x−5)
(5)(x+5)(x+2) (6)(x+1)(x+22) (7)Cannot be factored (8)(x−4)(x−3)
(9)(x+5)(x+3) (10)(x−16)(x−1) (11)Cannot be factored (12)(x−8)(x−5)
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(Challenge)Kim could know the signs of the factors without knowing the values ofbandcby
using this reasoning: ifbis negative, both factors ofcmust be negative. Ifbis positive, both
factors ofcmust be positive.
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