Algebra 2/Trig
8.4 Review
Factor each expression completely. Specify if it cannot be factored.
1.
𝑥 ! + 12𝑥 + 36
6.
9𝑘 ! − 24𝑘 + 16
2.
𝑛! − 1
7.
16𝑧 ! − 81
3.
28𝑥 ! − 7𝑥
8.
16𝑞! + 40𝑞 + 25
4.
𝑚! + 5𝑚 − 24
5.
−13𝑛! + 52
9. 𝑛! − !
!
10. 6𝑥 ! + 3𝑥 − 18
For questions 11-29, simplify each expression. State any restrictions.
11.
12.
13.
! ! !!
! ! !!!
16.
!!!!"!! !
! ! !!"
17.
!"!!! !
! ! !!!!
18.
14.
2 x 2 − 3x − 2
x2 − 5x + 6
19.
15.
x2 − 2 x − 8
3x 2 + 4 x − 4
20.
x 2 − 2x − 8 x + 3
⋅
x+3
x−4
!! ! !!!!!
!!!
!"!! !
∙ ! ! !!!!!"
4 x2 − 1
x2 − 6 x + 9
⋅
2 x2 − 5x − 3 2 x2 + 5x − 3
!!!
! ! !!!!!
! ! !!"
÷
! ! !!!!!"
! ! !!!!!
! ! !!!!!
÷ ! ! !!!!!
! ! !!!!!"
21. Which shape, a square or a circle, provides more efficient use of fencing to surround a garden if the side
length of the square is 2.5 times the radius of the circle? Use ratios and inequalities to prove the answer.
22. Which shape would have the greater area to perimeter ratio, a circle or an equilateral triangle? The area
!
!
of the triangle is 𝐴 = ! 𝑠 ! 𝑠 . Assume that the side length of the triangle is equal to the diameter of
the circle. Use ratios and inequalities to prove the answer.
Answers:
1.
2.
(𝑥 + 6)!
(𝑛 − 1)(𝑛! + 𝑛 + 1)
3.
7𝑥(2𝑥 − 1)(2𝑥 + 1)
4.
(𝑚 + 8)(𝑚 − 3)
5.
−13(𝑛 + 2)(𝑛 − 2)
6.
7.
8.
!
3𝑘 − 4
(4𝑧 − 9)(4𝑧 + 9)
!
4𝑞 + 5
!
!
!
!
9. (𝑛 − )(𝑛 + )
10. 3 𝑥 + 2 2𝑥 − 3
11.
12.
13.
14.
15.
16.
17.
18.
19.
!!!
!!!
!!!
!!!
; 𝑥 ≠ −2, 0
; 𝑥 ≠ −6, 6
!! !!!
!!!
!!!!
!!!
!!!
!!!!
; 𝑥 ≠ −2, 3
; 𝑥 ≠ 2, 3
; 𝑥 ≠ −2,
!
!
𝑥 + 2; 𝑥 ≠ −3, 4
!(!!!!)(!!!)
!!!
!!!
!!!
!
!
!
!
; 𝑥 ≠ ±3, − ,
–(!!!)
(!!!)(!!!)
!!!
; 𝑥 ≠ −5, −3, 4
; 𝑥 ≠ ±4, −3, 1
20.
; 𝑥 ≠ ±7, −3, −2, 1
!!!
21. The Square.
22. The Circle.