Page 587 - Algebra 1

A trinomial of the form ax2 + bx + c can also be factored by grouping. The trinomial is expressed as a polynomial with four terms so that it can be factored by grouping.
To express trinomials in the form ax2 + bx + c with four terms, first identify a,b,andc.Forexample,inthetrinomial2x2 +11x+15,a=2,b=11,and c = 15. Then, to factor a trinomial such as 2x2 + 11x + 15 by grouping, use the steps shown below.
Step 1: Find the product of ac.
2 · 15 = 30
Step 2: Find two factors of ac with a sum equal to b. 6 · 5 = 30 and 6 + 5 = 11
Step3: Writethetrinomialusingthesum.Replace11xwith6x+5x. 2x2 +11x+15=2x2 +6x+5x+15
Step4: Factorbygrouping.
2x2 +11x+15
=2x2 +6x+5x+15 =(2x2 +6x)+(5x+15) = 2x(x + 3) + 5(x + 3) = (x + 3)(2x + 5)
Factoring a Trinomial
Factor each trinomial by grouping.
a. x2-7x-44 SOLUTION
ac=1·-44=-44;Factorsof -44withasumof -7are-11and4. x2 -7x-44
Example
5
=x2 -11x+4x-44
= (x2 - 11x) + (4x - 44) = x(x - 11) + 4(x - 11) = (x - 11)(x + 4)
b. 6k2 -17k+10 SOLUTION
Replace-7xwith-11xand4x. Group into two binomials.
Factor out the GCF of each binomial. Factor out (x - 11).
Caution
Remember to change the signs of terms within the parentheses when factoring out negative 1.
572 Saxon Algebra 1
ac=6·10=60;Factorsof 60withasumof -17are-5and-12. 6k2 -17k+10
= 6k2 - 12k - 5k + 10
= (6k2 - 12k) - (5k - 10) = 6k(k - 2) - 5(k - 2)
= (k - 2)(6k - 5)
Replace -17k with -12k and -5k. Group into two binomials.
Factor out the GCF of each binomial. Factor out (k - 2).