When you factor out the GCF of a polynomial, sometimes the expression that remains
is a perfect-square trinomial or the difference of two squares. You can then factor this
expression further using the rules from this lesson...Jhf o k
ls 24g2 - 6 a
difference of tw o
squares?
No. 2 4 g 2 and 6 are not
perfect squares. To g e t
a d ifference o f squares,
you m u st firs t fa c to r o u t
the GCF.
Pr o b l em 5 Fac t o r i n g O u t a Co m m o n Fa ct o r
What is the factored form of 24g2 — 6?
24g2 - 6 = 6(4g 2 - 1 ) Fa cto r o u t th e GCF, 6.
= 6[(2g)2 - l2] W rite the difference as a 2 - fa2.
= 6(2g + l)(2g - 1) Use the rule for the difference of squares.Got It? 5. What is the factored form of each expression?
a. 12? 2 - 48 b. 12x 2 + 12x + 3J Lesso n Ch eck
Do y o u k n o w H OW?
Factor each expression.- y2 - 16y + 64
- 9 q2 + 12<7 + 4
- p2 36
- The area of a square is 36 w2 + 60 w + 25. What is the
side length of the square?
_ MATHEMATICAL
Do y o u UN DERSTAN D? PRACTICES
Identify the rule you would use to factor each expression.- 8 1 r2 - 9 0 r+ 25
- k2+ 12k + 36
- 9 h2 - 64
8. R e a s o n i n g Explain how to determine whether a
binomial is a difference of two squares.Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
PracticeMATHEMATICAL
PRACTICESFactor each expression.- h2 + 8h+ 16
- m2 + 18m + 81
- 64x2 + 112x + 49
- 36s2 - 6 0 s + 25
- v2 — lO iz + 25
- q2 + 2q + 1
- 4r 2 + 3 6 r+ 8 1
- 2 5 z 2 + 4 0 z + 1 6
See Problems 1 and 2.
11. d2 — 20d + 100- p2 - 4p + 4
17.9n2 — 42n + 49 - 49g 2 - 84g + 36
The given expression represents the area. Find the side length of the square(^2122). 23.
10Or2 - 2 20 r + 121 64r2 - 144r + 81 25 r 2 + 30r + 9
5 2 6 Chapter 8 Po/ ynomials and Factoring