Teaching Notes 5.18: Factoring Trinomials if the Leading
Coefficient Is an Integer Greater Than 1
IntegerGreaterThan1 5.18: Factoring Trinomials if the Leading Coefficient Is an
factors of the product, finding the appropriate sum, and then factoring by grouping. This can
prove to be a difficult task for students because students must find all of the factors.- Review factoring trinomials by presenting this example:x^2 + 5 x+4. Note that students
must find the factors of 4 whose sum equals 5. x^2 + 5 x+ 4 =(x+4)(x+1) - Contrast this with factoring 2x^2 − 11 x+12. Note that the leading coefficient is 2. To factor
this trinomial, students must find the product of both the coefficient ofx^2 andthethirdterm
of the trinomial. This product is 2×12 or 24. Students must identify two factors of 24 whose
sum is−11 and then factor by grouping. 2x^2 − 11 x+ 12 =(2x−3)(x−4) - Review the information and example on the worksheet with your students. Depending on
their abilities, you may find it helpful to review 5.17: ‘‘Factoring by Grouping.’’ Emphasize
that your students must find all of the factors ofac, including both the positive and negative
factors. From this list of factors, they should find a pair of factors whose sum is the middle
term. Remind them to always check their answers.
EXTRA HELP:
When you write the expression, you may have to rearrange terms so that there is a common
monomial factor.ANSWER KEY:
(1)(2x+3)(x+2) (2)(3x−1)(x+5) (3)Cannot be factored (4)(2x−1)(4x+3)
(5)(3x−1)(2x+3)
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(Challenge)Ronnie must select a pair of factors of−6 whose sum is−1, in this case−3and2.
------------------------------------------------------------------------------------------^6 x^2 −x−^1 =^6 x^2 +^2 x−^3 x−^1 =^2 x(3x+1)−(3x+1)=(2x−1)(3x+1)210 THE ALGEBRA TEACHER’S GUIDE