CHAPTER 8 REVIEW
Algebra 8
PROBLEM #1
Factor the monomial completely.
-33x y
2 3
ANSWER #1
−1 ∙ 3 ∙ 11 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦
PROBLEM #2
Find the GCF.
22b, 33c
ANSWER #2
GCF: 11
PROBLEM #3
Find the GCF.
21xy, 28x y, 42xy
2
2
ANSWER #3
GCF: 7𝑥𝑦
PROBLEM #4
A landscape architect is designing a stone path 36 inches
wide and 120 inches long. What is the maximum size
square stone that can be used so that none of the
stones have to be cut?
ANSWER #4
GCF: 12
The maximum size square is 12in x 12in
PROBLEM #5
Factor.
12x + 24y
ANSWER #5
12(𝑥 + 2𝑦)
PROBLEM #6
Factor.
14x y - 21xy + 35xy
2
2
ANSWER #6
7𝑥𝑦(2𝑥 − 3 + 5𝑦)
PROBLEM #7
Factor.
a - 4ac + ab - 4bc
2
ANSWER #7
(𝑎 + 𝑏)(𝑎 − 4𝑐)
PROBLEM #8
Factor.
2x - 3xz - 2xy + 3yz
2
ANSWER #8
(𝑥 − 𝑦)(2𝑥 − 3𝑧)
PROBLEM #9
Solve.
x(3x - 6) = 0
ANSWER #9
Set each factor = 0 then solve.
𝑥: {0, 2}
PROBLEM #10
Solve.
x = 3x
2
ANSWER #10
Bring 3x to the other side, factor, then set
each factor = 0 to solve for x.
𝑥: {0, 3}
PROBLEM #11
Factor.
x - 8x +15
2
ANSWER #11
Leading coefficient is 1 (a=1) so break
down the constant.
(𝑥 − 3)(𝑥 − 5)
PROBLEM #12
Factor.
x - 5x - 6
2
ANSWER #12
Leading coefficient is 1 (a=1) so break
down the constant.
(𝑥 + 1)(𝑥 − 6)
PROBLEM #13
Solve.
x - 5x - 50 = 0
2
ANSWER #13
Leading coefficient is 1 (a=1) so break
down the constant.
𝑥 + 5 𝑥 − 10 = 0
𝑥: {−5, 10}
PROBLEM #14
Solve.
x +12x + 32 = 0
2
ANSWER #14
Leading coefficient is 1 (a=1) so break
down the constant.
𝑥+4 𝑥+8 =0
𝑥: {−8, −4}
PROBLEM #15
Factor the trinomial, if possible. If the trinomial cannot
be factored, write prime.
12x + 22x -14
2
ANSWER #15
Factor out GCF.
Leading coefficient is not 1 (a>1) so make a
MAMA chart.
2 2𝑥 − 1 3𝑥 + 7
PROBLEM #16
Factor the trinomial, if possible. If the trinomial cannot
be factored, write prime.
2a +13a - 24
2
ANSWER #16
Leading coefficient is not 1 (a>1) so make a
MAMA chart.
𝑎 + 8 2𝑎 − 3
PROBLEM #17
Solve each equation. Check your solutions.
6x - 7x - 5 = 0
2
ANSWER #17
Leading coefficient is not 1 (a>1) so make a
MAMA chart.
3𝑥 − 5 2𝑥 + 1 = 0
1 5
𝑥: {− , }
2 3
PROBLEM #18
Solve each equation. Check your solutions.
40x + 2x = 24
2
ANSWER #18
Bring over 24 to the other side.
Factor out GCF
Leading coefficient is not 1 (a>1) so make a
MAMA chart.
2 5𝑥 + 4 4𝑥 − 3
PROBLEM #19
Factor each polynomial.
3x - 3
2
ANSWER #19
Factor out GCF.
3(𝑥 2 − 1)
Now you have difference of two perfect
squares so break down further.
3(𝑥 + 1)(𝑥 − 1)
PROBLEM #20
Factor each polynomial.
16a - 21b
2
2
ANSWER #20
Prime
PROBLEM #21
Solve by factoring. Check your solutions.
9x - 25 = 0
2
ANSWER #21
3𝑥 + 5 3𝑥 − 5 = 0
5 5
𝑥: {− , }
3 3
PROBLEM #22
Solve by factoring. Check your solutions.
x - 4 =12
2
ANSWER #22
𝑥+4 𝑥−4 =0
𝑥: {−4, 4}
PROBLEM #23
Factor each polynomial, if possible. If the polynomial
cannot be factored write prime.
x + 5x + 25
2
ANSWER #23
Prime
PROBLEM #24
Factor each polynomial, if possible. If the polynomial
cannot be factored write prime.
4 - 28a + 49a
2
ANSWER #24
Perfect square trinomial
2 − 7𝑎 2
PROBLEM #25
Factor each polynomial, if possible. If the polynomial
cannot be factored write prime.
x -16x
4
2
ANSWER #25
Factor out GCF.
𝑥 2 (𝑥 2 − 4)
Then you have difference of two perfect
squares, so factor more.
𝑥 2 (𝑥 + 2)(𝑥 − 2)
PROBLEM #26
Solve each equation. Check your solutions.
4y = 64
2
ANSWER #26
Bring 64 to the other side.
Factor out GCF.
4 𝑦 2 − 16 = 0
Then you have difference of two perfect squares, so
factor more.
4 𝑦−4 𝑦+4 =0
Set each factor = 0 and solve for y.
𝑦: {−4, 4}
PROBLEM #27
Solve each equation. Check your solutions.
(x - 9) =144
2
ANSWER #27
FOIL left side and bring 144 to the other
side.
You have a trinomial where a=1, so break
down c.
𝑥 + 3 𝑥 − 21 = 0
Then, set each factor =0 and solve for x.
𝑥: {−3, 21}
PROBLEM #28
A sidewalk of equal width is built around a square yard.
What is the width of the sidewalk?
ANSWER #28
6 + 2𝑥 2 = 900
36 + 24𝑥 + 4𝑥 2 = 900
−864 + 24𝑥 + 4𝑥 2 = 0
4𝑥 2 + 24𝑥 − 864 = 0
4 𝑥 2 + 6𝑥 − 216 = 0
4 𝑥 − 12 𝑥 − 18 = 0
𝑥: {12, 18}