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Math 9
Review of Factoring
MOM PAGE 364
Lesson 29(4)
Name SOLUTIONS
2. Write a polynomial that represents the perimeter and a polynomial that represents the
area of each rectangle.
Perimeter = 2(x + 4) + 2(x)
= 2x + 8 + 2x
= 4x + 8
Area = x(x + 4)
= x2 + 4x
Perimeter = 2(2x + 3) + 2(x + 1)
= 4x + 6 + 2x + 2
= 4x + 2x + 6 + 2
= 6x + 8
Perimeter = 2(x + 5) + 2(2x + 1)
= 2x + 10 + 4x + 2
= 2x + 4x + 10 + 2
= 6x + 12
Area = (2x + 3)(x + 1)
= 2x2 + 2x + 3x + 3
= 2x2 + 5x + 3
Area = (2x + 1)(x + 5)
= 2x2 + 5x + x + 5
= 2x2 + 6x + 5
7. Simplify.
a) (5x2 – 3y2) + (x2 + 4y2)
b) (-2x – 7) – (-14x – 6) c) (8a2 + 2a – 3) – (-6a2 + 4a + 7)
d) (3x – 2) – (x – 1) + (4x – 3)
e) (4x2 – 3x) – (x2 + 2x) + (3x2 – x)
f) (3x2 + 5x + 7) – (2x2 – 4x + 9)
(5x2 – 3y2) + (x2 + 4y2)
5x2 – 3y2 + x2 + 4y2
5x2 + x2 – 3y2 + 4y2
6x2 + y2
(8a2 + 2a – 3) – (-6a2 + 4a + 7)
8a2 + 2a – 3 + 6a2 – 4a – 7
8a2 + 6a2 + 2a – 4a – 3 – 7
14a2 – 2a - 10
(4x2 – 3x) – (x2 + 2x) + (3x2 – x)
4x2 – 3x – x2 - 2x + 3x2 – x
4x2 – x2 + 3x2 – 3x - 2x – x
6x2 – 6x
(-2x – 7) – (-14x – 6)
-2x – 7 + 14x + 6
-2x + 14x – 7 + 6
12x - 1
(3x – 2) – (x – 1) + (4x – 3)
3x – 2 – x + 1 + 4x – 3
3x – x + 4x – 2 + 1 – 3
6x - 4
(3x2 + 5x + 7) – (2x2 – 4x + 9)
3x2 + 5x + 7 – 2x2 + 4x – 9
3x2 – 2x2 + 5x + 4x + 7 – 9
x2 + 9x - 2
9. Simplify.
a) (-25n2)(8n2)
b) (-35c3)(-4c2)
-200n4
140c5
c) (17x2)(5x3)
d) (-28n)(5n3)
85x5
-140n4
10. Simplify.
 45 y 6
a)
 5y4
3n 6
b)
5n 4
e) 18 x 4  3x
f) (52 y 6 )  13 y 5
9y2
25 x 4
c)
 5x 4
-5
3n 2
5
6x3
3c 3
2
36c 5
d)
24c 2
-4y
12. Expand.
a) 4(y – 2)
b) 8(a – 3)
c) -4(x + 2)
d) 3x(5 – x)
e) 2y(y – 6)
f) (-5x)(3 – x)
g) 5y(7 – 2y + 3y2)
h) (-6x)(3x2 + 5x – 12)
4y – 8
15x – 3x2
35y – 10y + 15y3
8a – 24
2y2 – 12y
-18x3 – 30x2 + 72x
-4x – 8
-15x + x2
MOM PAGE 365
13. Expand.
a) 3c(5 – 2c)
b) (-4n)(2n – 1)
e) 5s(3s2 – 2s – 7)
f) 3p2(2 – 3p – p2)
15c – 6c2
18k – 6k2 + 6k3
c) (-7y)(2y2 – 5)
-8n2 + 4n
15s3 – 10s2 – 35s
d) 6k(3 – k + k2)
-14y3 + 35y
6p2 – 9p3 – 3p4
14. Factor each polynomial.
a) 5y – 10
b) 12a + 18
e) 4w + 3w2 – 7w3
f) 8y3 – 4y2 + 2y
5(y – 2)
2(a2 – 5a + 1)
c) -3x2 + 6x – 12
d) 2a2 – 10a + 2
3(-x2 + 2x – 4)
2y(4y2 – 2y + 1)
6(2a + 3)
w(4 + 3w – 7w2)
15. Factor. Check by expanding.
a) 6y + 18y2
b) -3a + 12a2
c) 5a2 – 25a3
e) 3m – 9m2 + 15m3 f) 12k2 – 48k4 – 18k6
d) 3a3 + 4a2 + 7a
g) 6x2y – 3xy + 9xy2
h) 8ab – 4a2b2 + 6ab2
6y(1 + 3y)
a(3a2 + 4a + 7)
3xy(2x – 1 + 3y)
-3a(-1 – 4a)
3m(1 – 3m + 5m2)
2ab(4 – 2ab + 3b)
5a2(1 – 5a)
6k2(2 – 8k2 – 3k4)
18. Expand.
a) (x – 3)(x – 4)
b) ( y + 7)(y + 3)
c) (a – 2)(a + 5)
d) (n – 6)(n + 7)
e) (n + 4)(n – 7)
f) (x – 1)(x + 5)
g) (2x + 3)(x – 4)
h) (3a + 1)(2a + 5)
x2 – 4x – 3x + 12
x2 – 7x + 12
n + 7n – 6n – 42
n2 + n – 42
2x2 – 8x + 3x – 12
2x2 – 5x – 12
y2 + 3y + 7y + 21
y2 + 10y + 21
n2 – 7n + 4n – 28
n2 – 3n – 28
6a2 + 15a + 2a + 5
6a2 + 17a + 5
a2 + 5a – 2a – 10
a2 + 3a - 10
x2 + 5x – x – 5
x2 + 4x - 5
21. Factor.
a) x2 + 10x + 16
b) a2 + 4a – 12
e) x2 – x – 12
f) a2 + a – 30
(x + 2)(x + 8)
(c – 7)(c + 5)
(a + 6)(a – 2)
(x – 4)(x + 3)
c) x2 – 10x + 25
d) c2 – 2c – 35
(x – 5)(x – 5)
(a + 6)(a – 5)
22. Factor.
a) x2 – 7x + 10
b) y2 + 6y + 9
e) 8 + 7x – x2
f) n2 + 3n – 40
(x – 5)(x – 2)
(5 – x)( 3 + x )
c) x2 + 6x + 5
(y + 3)(y + 3)
(8 – x)(1 + x )
d) 15 + 2x – x2
(x + 5)(x + 1)
(n + 8)(n – 5)
23. Factor completely.
a) 2x2 – 12x – 72
b) 5m2 + 10m – 40
c) y3 + 2y2 – 3y
e) 4m3 – 40m2 + 100m
f) -2b3 – 14b2 – 24b
2(x2 – 6x – 36)
5(m2 + 2m – 8)
5(m + 4)(m – 2)
4m(m2 – 10m + 25)
4m(m – 5)(m – 5)
a(a2 -3a – 10)
a(a – 5)(a + 2)
d) a3 – 3a2 – 10a
y(y2 + 2y – 3)
y(y + 3)(y – 1)
-2b(b2 + 7b + 12)
-2b(b + 3)(b + 4)
24. Simplify, then factor completely.
a) 4x2 – 2x – 6 + 10x – 3x2 – 3
b) 5x + 6 – 5x2 + 4 – 12x + 6x2
c) 30 – 2y – y2 + 5 + 14y + 2y2
d) 7a – 10 – 2a – 4 + a2
e) 6m2 – 2m – 1 – 4m2 + 8m – 7
f) 2x – 12 – 8x2 – 8x – 12 + 11x2
4x2 – 3x2 – 2x + 10x – 6 – 3
x2 + 8x – 9
(x + 9)(x – 1)
2y2 – y2 – 2y+ 14y + 30 + 5
y2 + 12y + 35
(y + 7)(y + 5)
6m2 – 4m2 + 8m – 2m – 1 – 7
2m2 + 6m – 8
2(m2 + 3m – 4)
2(m + 4)(m – 1)
-5x2 + 6x2 + 5x – 12x + 6 + 4
x2 – 7x + 10
(x – 5)(x – 2)
a2 + 7a – 2a – 10 – 4
a2 + 5a – 14
(a + 7)(a – 2)
-8x2 + 11x2 + 2x – 8x – 12 – 12
3x2 – 6x – 24
3(x2 – 2x – 8)
3(x – 4)(x + 2)