@ Common Core State Standards
_l_ _l_ ~ A-SSE.A.1 a Interpret parts of an expression, such as
factoring OX + OX T C terms, factors, and coefficients.
MP 1, MP 2, M P3, M P4Objective To factor trinom ials of th e form ax 2 + bx + cGet t i n g Read y!An ar r ay of t h r ee rect angular solar
panels has area 3x2 + 21x + 36.
The height of t he array is x + 3.
What is the length of the array?
youdid fo r Ex p l a i n y o u r r e a so n i n g.
one panel in
Lesson 8 -5 —now
th e re are more., M A T H E M A T I C A L
1 P R A C T I C E S
Essent ial Und er st and ing You can write som e trinom ials of th e form
ax2 + bx + c as the p ro d u ct of two binom ials.C onsider the trinom ial 6 x 2 + 23x + 7. To factor it, th in k of 23x as 2x + 21x.
6x2 + 23x + 7 = 6x2 + 2x + 21x + 7 Rewrite 23x as 2x + 21x.
= 2x(3x + 1) + 7(3x + 1) Factor out the GCF of each pair o f terms.
= (2x + 7)(3x + 1 ) D istributive PropertyHow do you know to rew rite 23x as 2x + 21x? Notice th a t m ultiplying 2 a n d 21 gives
42, w hich is the p ro d u ct of th e x 2-coefficient 6 an d th e co n stan t term 7. This example
suggests that, to factor a trinom ial of th e form ax2 + bx + c, you should look for factors
of th e p ro d u ct ac th at have a sum of b.Will the process still
w o rk if you w r it e
5 x 2 + 10x + x + 2?
Yes. You can re w rite th is
a lte rn a te expression as
5x(x + 2) + (x + 2),
which equals
(5x + 1)(x + 2).Problem 1 Fact o r i n g W h e n a c I s Po si t i v e
W hat is th e fa cto red fo rm o f 5 x 2 + l l x + 2?
S te p 1 Find factors of ac t h a t h a v e s u m b.
Since ac = 10 and b = 11, find positive
factors of 10 th at have sum 11.
S te p 2 To factor th e trinom ial, use the factors you
found to rew rite bx.
5x2 + l l x + 2 = 5x2 + lx + lOx + 2 Rewrite bx: Tlx = 1x + 10x.
= x(5x + 1) + 2(5x + 1) Factor out the GCF of each pair o f terms.
= (x + 2)(5x + 1) Distributive PropertyFactors o f 10 1,10 :: 2,5
Sum o f Factors^11 7518 Chapter 8 Po l yn o m ial s an d Fact o r in g