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Worksheets

Factoring Polynomials

Total questions: 225

Worksheet time: 12hrs 38mins

Name
Class
Date
1.
What is the GCF? 12x+8
a)
12
b)
8
c)
4
d)
x
2.
What is the GCF? 5x2+20x
a)
5
b)
x
c)
5x
d)
20x
3.

Factor by using GCF:

8n3 + 2n2

a)

2n2(4n-1)

b)

2n2(4n + 1)

c)

n2(8n+2)

d)

3n(4n+1)

4.

Factor by using GCF:

8r3 + 16r2

a)

4r2(2r + 4)

b)

8r2(r + 2)

c)

8(r3 + r2)

d)

4(r3 + 2r2)

5.
Factor Completely: x2-17x+72
a)
(x-9)(x+8)
b)
(x-9)(x-8)
c)
x(x-3)
d)
(x+9)(x+8)
6.
Factor Completely: x2-7x-8
a)
(x+1)(x-8)
b)
(x+1)(x+8)
c)
5(x+4)(x+5)
d)
(x-1)(x+8)
7.
Factor Completely: 2k2-14k-60
a)
2(k-10)(k-3)
b)
Not Factorable
c)
(k-5)(k+9)
d)
2(k-10)(k+3)
8.
Factor Completely: x2+13x+40
a)
(x+5)(x+8)
b)
5x(x+3)
c)
3x(x+6)
d)
x(x-4)
9.
Factor
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
10.
Factor
3x² + 17x + 10
a)
(3x-2)(x-5)
b)
(3x+2)(x+5)
c)
(3x-5)(x-2)
d)
(3x+5)(x+2)
11.

Factor:

2m² + 3m - 9

a)

(2m - 1)(m + 9)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

12.

Factor:

6x² + 5x - 6

a)

(6x + 1)(x - 6)

b)

(6x + 6)(x - 1)

c)

(2x - 3)(3x + 2)

d)

(3x - 2)(2x + 3)

13.

Factor.

5x2 - 7x + 2

a)

(5x - 2)(x + 1)

b)

(5x + 2)(x + 1)

c)

(7x - 1)(x - 4)

d)

(5x - 2)(x - 1)

14.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Group

15.
Factor the polynomial:
5x2 - 13x + 6
a)
(x + 3)(5x - 2)
b)
(x - 2)(5x - 3)
c)
(x + 2)(5x + 3)
d)
(x - 3)(5x + 2)
16.

Factor:

x2 + 9x − 36

a)

(x + 12)(x − 3)

b)

(x + 9)(x − 4)

c)

(x − 12)(x + 3)

d)

(x − 9)(x − 4)

17.
Factor
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
18.
Factor:
 4h² - 17h + 4
a)
(2h - 2)²
b)
4(h + 4)(h + 1)
c)
(2h - 2)(2h + 2)
d)
(h - 4)(4h - 1)
19.

Factor the Trinomial

a)

(4x+6)(x+3)\left(4x+6\right)\left(x+3\right)

b)

(4x−3)(x+3)\left(4x-3\right)\left(x+3\right)

c)

(x−3)(x−3)\left(x-3\right)\left(x-3\right)

d)

(4x+3)(x−3)\left(4x+3\right)\left(x-3\right)

20.

Factor the Trinomial

**Don't forget to look for GCF**

a)

(x+2)(x+2)\left(x+2\right)\left(x+2\right)

b)

2(x+4)(x+4)2\left(x+4\right)\left(x+4\right)

c)

(2x+1)(2x−1)\left(2x+1\right)\left(2x-1\right)

d)

2(x+2)(x+2)2\left(x+2\right)\left(x+2\right)

21.

What is the Greatest Common Factor of 24 and 54?

(a)  

22.

What is the GCF of 20, 24, and 40?

(a)  

23.

What is the GCF of x2 and  x9x^2\ and\ \ x^9 ?

a)

x2x^2  

b)

x7x^7  

c)

x11x^{11}  

d)

x18x^{18}  

24.

What is the GCF of xy10, x4y6, x9y9, and x10y10xy^{10},\ x^4y^6,\ x^9y^{9,\ and}\ x^{10}y^{10} ?

a)

xyxy^{ }  

b)

xy6xy^6  

c)

x4y4x^4y^4  

d)

x4y6x^4y^6  

25.

What are the complete factors of the polynomial 7x - 7 ?

(a)  

26.

What are the complete factors of 2x6 − 12x42x^{6\ }-\ 12x^4 ?

a)

2(x4−6x4)2\left(x^4-6x^4\right)  

b)

2x5(x−6x)2x^5\left(x-6x\right)  

c)

2x4(x2−6)2x^4\left(x^2-6\right)  

d)

x6(2x2−12)x^6\left(2x^2-12\right)  

27.

Which of the following is a perfect square expression?

a)

3x23x^2  

b)

4x4x  

c)

9x39x^3  

d)

16x416x^4  

28.

If one factor of the difference of two squares is x + 2, what is the other factor?

a)

x−2x-2  

b)

x2−2x^2-2  

c)

x2−22x^2-2^2  

d)

(x−2)2\left(x-2\right)^2  

29.

What is the complete factored form of z2−16z^2-16 ?

a)

(z−4)2\left(z-4\right)^2  

b)

(z−8)2\left(z-8\right)^2  

c)

(z−4)(z−4)\left(z-4\right)\left(z-4\right)  

d)

(z+4)(z−4)\left(z+4\right)\left(z-4\right)  

30.

What is the complete factored form of the expression y4−49y^4-49 ?

a)

(y2)2−(72)2\left(y^2\right)^2-\left(7^2\right)^2  

b)

(y2−7)2\left(y^2-7\right)^2  

c)

(y2+7)2\left(y^2+7\right)^2  

d)

(y2−7)(y2+7)\left(y^2-7\right)\left(y^2+7\right)  

31.

Which Of the following polynomials has factors (xy−1)(xy+1)\left(xy-1\right)\left(xy+1\right)  ?

a)

x2y−1x^2y-1  

b)

x2y2−1x^2y^2-1  

c)

xy2−1xy^2-1  

d)

x2y2+1x^2y^2+1  

32.

Which of the following expressions is a perfect cube?

a)

8x8x  

b)

27x227x^2  

c)

64x664x^6  

d)

125x4125x^4  

33.

Which of the following is the complete factored form of the cubic polynomial x3−8x^3-8 ?

a)

(x−2)(x2+2x+4)\left(x-2\right)\left(x^2+2x+4\right)

b)

(x+2)(x2−2x+4)\left(x+2\right)\left(x^2-2x+4\right)  

c)

(x−2)(x2+2x−4)\left(x-2\right)\left(x^2+2x-4\right)  

d)

(x−2)(x2−2x+4)\left(x-2\right)\left(x^2-2x+4\right)  

34.

Factor completely 27x3+64y327x^3+64y^3  

a)

(3x)3+(4y)3\left(3x\right)^3+\left(4y\right)^3  

b)

(3x+4y)(9x2−12xy+16y2)\left(3x+4y\right)\left(9x^2-12xy+16y^2\right)

c)

(3x+4y)(3x2−3xy+16y2)\left(3x+4y\right)\left(3x^2-3xy+16y^2\right)  

d)

(3x+4y)(3x2−12xy+4y2)\left(3x+4y\right)\left(3x^2-12xy+4y^2\right)  

35.

Your classmate was asked to square (2x−3)\left(2x-3\right)  , he answered 4x2−94x^2-9  .

Is his answer correct?

a)

Yes, because product rule is correctly applied.

b)

Yes, because squaring a binomial always produces a binomial product.

c)

No, because the answer must be 4x2+94x^2+9  .

d)

No, because squaring a binomial always produces a trinomial product.

36.

Find the factors of the given number.

8

(a)  

37.

Find the factors of the given number.

2x

(a)  

38.

Find the factors of the given number.

5ab

(a)  

39.

Find the factors of the given number.

12z

(a)  

40.

Find the factors of the given number.

20xy

(a)  

41.

What is the process of finding the factors of an expression which is the reverse process of multiplication?

(a)  

42.

What is the Greatest Common Factor of 12 and 24?

(a)  

43.

Which of the following pair of numbers has a GCF of 6?

a)

2 and 3

b)

8 and 12

c)

6 and 10

d)

12 and 18

44.

What is the GCF of 2a3 and a62a^{3\ }and\ a^6  ?

a)

a3a^3  

b)

2a32a^3  

c)

a6a^6  

d)

2a62a^6  

45.

What is the GCF of a5b8, a4b6, a3b9 and a12b10a^5b^8,\ a^4b^6,\ a^3b^9\ and\ a^{12}b^{10}  ?

a)

a5b8a^5b^8  

b)

a3b6a^3b^6  

c)

a12b8a^{12}b^8  

d)

a12b6a^{12}b^6  

46.

All of the following are factors of 12x212x^2  , except one. What is it?

a)

12

b)

12x

c)

12x212x^2  

d)

12x312x^3  

47.

What is the GCF of the expression 4x4+6x4x^4+6x  ?

a)

22  

b)

xx  

c)

2x2x  

d)

2x42x^4  

48.

If one factor of 4x2+64x^2+6  is 2, what is the other factor?

a)

2x+32x+3  

b)

4x+64x+6  

c)

2x+62x+6  

d)

2x2+32x^2+3  

49.

If one factor of 6ab2−12a2b3 is 1−2ab6ab^2-12a^2b^3\ is\ 1-2ab  , what is the other factor?

a)

6ab6ab  

b)

6a2b6a^2b  

c)

6ab26ab^2  

d)

6a2b26a^2b^2  

50.

Which of the following is a perfect square?

a)

12x412x^4  

b)

16x2y216x^2y^2  

c)

25x5y625x^5y^6  

d)

36x6y736x^6y^7  

51.

Which of the following expressions has factors (2x−y)and (2x+y)\left(2x-y\right)and\ \left(2x+y\right)  ?

a)

2x2+y22x^2+y^2  

b)

2x2−y22x^2-y^2  

c)

4x2+y24x^2+y^2  

d)

4x2−y24x^2-y^2  

52.

Using the pattern for factoring the sum of cubes, we know that factoring 8+b38+b^3  gives

a)

(2−b)(4−2b+b2)\left(2-b\right)\left(4-2b+b^2\right)  

b)

(2−b)(4+2b+b2)\left(2-b\right)\left(4+2b+b^2\right)  

c)

(2+b)(4−2b+b2)\left(2+b\right)\left(4-2b+b^2\right)  

d)

(2+b)(4+2b+b2)\left(2+b\right)\left(4+2b+b^2\right)  

53.

What is the complete factored from of 9x3−64y39x^3-64y^3  ?

a)

(3x−4y)(9x2+12xy+16y2)\left(3x-4y\right)\left(9x^2+12xy+16y^2\right)  

b)

(3x+4y)(9x2+12xy+16y2)\left(3x+4y\right)\left(9x^2+12xy+16y^2\right)  

c)

(3x−4y)(9x2−12xy+16y2)\left(3x-4y\right)\left(9x^2-12xy+16y^2\right)  

d)

(3x+4y)(9x2−12xy+16y2)\left(3x+4y\right)\left(9x^2-12xy+16y^2\right)  

54.

What is the complete factored form of 10+270y310+270y^3  ?

a)

10(1+3y)(1+3y+9y2)10\left(1+3y\right)\left(1+3y+9y^2\right)  

b)

10(1+3y)(1−3y+9y2)10\left(1+3y\right)\left(1-3y+9y^2\right)  

c)

10(1−3y)(1+3y+9y2)10\left(1-3y\right)\left(1+3y+9y^2\right)  

d)

10(1−3y)(1−3y+9y2)10\left(1-3y\right)\left(1-3y+9y^2\right)  

55.

The area of a rectangular garden is 9t2−649t^2-64  square units.

If one side is 3t−83t-8  , what is the other side?

a)

3t−83t-8  

b)

3t+83t+8  

c)

t−8t-8  

d)

t+8t+8  

56.
Factor f(x)= 2x²+32x+128
a)
(x+4)²
b)
(x-4)²
c)
(x+8)²
d)
(x-8)²
57.
Fully Factor the Following
25x2-81
a)
(5x-9)2
b)
(5x+9)(5x-9)
c)
25(x-9)2
d)
(9x+5)(9x-5)
58.
Fully Factor the Following
8x3-27
a)
(2x+3)(4x2-6x+9)
b)
(2x-3)(4x2+6x+9)
c)
(2x-3)(4x2+6x-9)
d)
(2x-3)(2x2+6x+9)
59.
Fully Factor the Following
4x2-16
a)
(2x-4)(2x+4)
b)
(4x-4)(4x+4)
c)
4(x-2)2
d)
4(x-2)(x+2)
60.
Factor
4b5+4b3+16b2
a)
4b3(b4+b2+4b)
b)
4b3(b4+4b+5)
c)
4(b5+b3+4b2)
d)
4b2(b3+b+4)
61.
Factor
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
62.
Find the product. 
   
(x - 10)2
a)
x2 - 100
b)
x2 - 20x + 100
c)
x2 - 20x +20
d)
x2 - 100x + 20
63.
Find the product.
 
(2x + 5)(2x - 5)
a)
4x2 - 25
b)
4x2 + 25
c)
4x2 - 20x - 25
d)
4x2 +20x - 25
64.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
65.
Factor:
x2 + 7x - 30
a)
(x + 10)(x - 7)
b)
(x - 10)(x + 3)
c)
(x + 10)(x + 3)
d)
(x + 10)(x - 3)
66.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
67.
Factor
a2 - a - 12
a)
(a - 4)(a + 3)
b)
(a + 6)(a - 4)
c)
(a - 6)(a + 4)
d)
(a + 4)(a - 3)
68.
Factor:
x2 + 0x - 144
a)
(x + 12)2
b)
(x - 12)(x + 12)
c)
(x - 12)2
d)
122
69.
Factor
x2 -16x + 48
a)
(x - 12)(x - 4)
b)
(x + 6)(x - 8)
c)
(x + 12)(x - 4)
d)
(x -16)(x - 3)
70.
Factor:
p2 - 14p
a)
p(1 - 14)
b)
2p(p - 7)
c)
p2(1-14)
d)
p(p - 14)
71.
What do you call a polynomial that cannot be factored?
a)
FOIL
b)
Simplified
c)
Prime
d)
Proper
72.
What is a method of checking your work when factoring?
a)
FOIL
b)
asking the teacher every time
c)
assume you're correct
d)
division
73.
What is the GCF of the trinomial?
3x2 - 9x -120
a)
3
b)
2
c)
6
d)
9
74.
Which is another way of correctly expressing
 (x  - 3)(x - 3)?
a)
(x2 - 32)
b)
(x2 - 3)
c)
(x + 3)(x - 3)
d)
(x - 3)2
75.
Factor completely: 
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
76.
Factor
10x2 + 15x-5
a)
25(10x3+45x-15)
b)
5(2x3 + 3x2-x)
c)
x(10x3+15x-5)
d)
5(2x2+3x-1)
77.
Factor
k2+7x+10
a)
(k+2)(k+5)
b)
(k-2)(k-5)
c)
(k+10)(k+4)
d)
(k+2)(k-5)
78.
Factor
n2 + 16n + 63
a)
(n-7)(n+4)
b)
(n+7)(n-9)
c)
(n-3)(n-10)
d)
(n+7)(n+9)
79.
Factor
k2 -2k - 24
a)
(k+4)(k-6)
b)
(k+4)(k+6)
c)
(k+6)(k-1)
d)
(k-4)(k+6)
80.
Factor
2x2 - 13x - 70
a)
(2x-7)(x+10)
b)
(7x+5)(x+2)
c)
(2x+7)(x-10)
d)
2(x+7)(x+10)
81.
Factor
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
82.
Factor
81m2 - 1 
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
83.
12x + 9
a)
3(4x + 3)
b)
x(12+9)
c)
3(4x - 3)
d)
not factorable
84.
17xy - x
a)
17(xy - x)
b)
y(17x - x)
c)
x(17y - 1)
d)
not factorable
85.
The area of a rectangle is (6x2+7x+2) square inches and the length is (3x+2) inches. Which expression represents the rectangle's width?
HINT: Area goes INSIDE the box, width & length go on the SIDES of the box
a)
(2x+2) inches
b)
(2x-2) inches
c)
(2x+1) inches
d)
(2x-1) inches
86.
A square has an area of 25x2+20x+4 square feet. Find the length of the square.
HINT: Squares have equal sides...square each binomial!
a)
(x+2) meters
b)
(x-2) meters
c)
(5x+2) meters
d)
(5x-2) meters
87.
Which binomial is a factor of 26x2-43x+6?
HINT: You must factor this by hand. Factors of 26*6=156 that ADD to -43 are -4 and -39.
a)
2x-3
b)
2x+3
c)
2x-2
d)
2x+2
88.
Which binomials are a difference (subtraction) of two squares?
I. 6a2-25
II. 4x2+16
III. b2-9
IV. 49y2-64
a)
I only
b)
III only
c)
III and IV
d)
II, III, and IV
89.
Factor x2-x-72
a)
(x-9)(x+8)
b)
(x+9)(x-8)
c)
(x+9)(x-8)
d)
(x-9)(x-8)
90.
Factor x2-11x-60
a)
(x-12)(x-5)
b)
(x-15)(x+4)
c)
(x-15)(x-4)
d)
(x+12)(x-5)
91.
Factor x2-14x+24
a)
(x-8)(x+3)
b)
(x+12)(x-2)
c)
(x+8)(x+3)
d)
(x-12)(x-2)
92.
Factor x2-2x-15
a)
(x+5)(x-3)
b)
(x-5)(x-3)
c)
(x-5)(x+3)
d)
(x+5)(x+3)
93.
Factor x2+4x-32
a)
(x+8)(x-4)
b)
(x-8)(x-4)
c)
(x-8)(x+4)
d)
(x+8)(x+4)
94.
x2-x-12
a)
(x+6)(x+2)
b)
(x-4)(x+3)
c)
(x+4)(x+3)
d)
(x-4)(x-3)
95.
w3 + 3w
a)
3w(1)
b)
w(w2 + 3)
c)
w3(w + 3)
96.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
97.
Factor completely: 3x² - 7x + 2
a)
(x - 1) (3x + 2)
b)
(x - 2) (3x -1)
c)
(x - 1) (3x - 2)
d)
(x + 2) (3x + 1)
98.
Factor Completely: 2x² + x - 6
a)
(x + 2) (2x -3)
b)
(x - 6) (2x + 1)
c)
(x + 1) (2x - 6)
d)
(x - 2) (2x + 3)
99.
Factorly Completely: 2x² - 7x + 6
a)
(x -1)(2x - 6)
b)
(x - 3) (2x - 2)
c)
(x - 2) (2x - 3)
d)
(x - 6) (2x - 1)
100.
Factor completely: 2x² - 3x - 2
a)
(2x - 2)(x + 1)
b)
(2x + 1)(x - 2)
c)
(2x - 1)(x - 2)
d)
(2x - 1) (x - 1)
101.
Factor Completely: 3x² + 5x - 12
a)
(3x + 4)(x-3)
b)
(3x - 4)(x + 3)
c)
(3x + 3)(x -4)
d)
(3x - 3)(x + 4)
102.

Factor by grouping

x3 - 4x2 -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x2 -4)

c)

(x+4)(x2 -4)

d)

(x-4)(x-2)

103.
Factor by GCF:
63x4 - 7x2 + 28x
a)
7x(9x2 - 7 + 4x)
b)
x(63x3 - 7x + 28)
c)
7x(9x3 - x + 4)
d)
not factorable
104.
Factor by grouping:
5n³-10n²+3n-6
a)
(5n²+3)(n-2)
b)
(5n²-3)(n-2)
c)
(5n³+3)(n-2)
d)
10n(n²-6)
105.
Factor by grouping:
x³+7x²-2x-14
a)
(x²-2)(x-7)
b)
(x²+2)(x-7)
c)
(x²+2)(x+7)
d)
(x²-2)(x+7)
106.
Factor by grouping:
4p³+8p²+3p+6
a)
(2p²+3)(p+2)
b)
(2p²+6)(p+4)
c)
(4p²+3)(p+2)
d)
(4p²+8p)(3p+6)
107.
a)
(4n+3)(4n-3)
b)
(16n+9)(16n-9)
c)
(4n-3)2
d)
(4n+3)2
108.
k4 -36
a)
(k2+6)(k2-6)
b)
(k2-6)2
c)
(k-6)4
d)
(k+6)(k-6)
109.
12p3-21p2+28p-49
a)
(3p2+7)(4p-7)
b)
(4p2+7)(3p-7)
c)
(2p+5)(2p-2)(3p+7)
d)
no clue
110.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
111.
Factor completely: 
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
112.
Factor completely.
2n2 + 13n + 15
a)
(5n - 9)(n - 3)
b)
(3n + 7)(n + 4)
c)
(2n + 3)(n + 5)
d)
Not factorable
113.
Factor completely.
2n2 + n - 6
a)
(2n + 7)(n - 9)
b)
Not factorable
c)
(2n - 3)(n - 2)
d)
(2n - 3)(n + 2)
114.
Factor completely.
3x2 - 75
a)
3( x + 5 ) ( x - 5 ) 
b)
Not factorable
c)
( x + 5 ) ( x - 5 ) 
d)
3( x - 5 ) ( x - 5 ) 
115.
Factor:
 2m² + 3m - 9
a)
2(m + 3)(m - 3)
b)
(2m - 3)²
c)
(m + 3)(2m - 3)
d)
(2m + 3)(m - 3)
116.
Factor:
 x2 - 15x + 50
a)
(x - 10)(x - 15)
b)
(x - 10)(x - 5)
c)
(x - 25)2
d)
(x - 5)2
117.
A classroom has an area of 3x2 + 7x + 2. If the length of the classroom is (3x + 1), what is the width of the classroom?
a)
3x + 1
b)
x + 2
c)
3x + 7
d)
7x + 2
118.
The area of a rectangle is   (x2 + 17x+42) ft2. If its width is (x + 3) ft. What is its length?
a)
(x + 17) ft
b)
(x + 14) ft
c)
(x - 14) ft
d)
(x - 17) ft
119.
Factor:
 2m² + 3m - 9
a)
2(m + 3)(m - 3)
b)
(2m - 3)²
c)
(m + 3)(2m - 3)
d)
(2m + 3)(m - 3)
120.
What is a letter that represents an unknown number?
a)
Vocabulary
b)
Variable
c)
Constant
d)
Coefficient
121.
Terms in a polynomial are separated by what?
a)
Parenthesis
b)
Multiply/Divide 
c)
Constants
d)
Add/Subtract
122.
Which of the following are examples of like terms?
a)
2 and 2x
b)
y3 and x3
c)
y and x
d)
-3x and 3x
123.
What is a mix of variables, constants, and operations that do NOT have an equal sign?
a)
Equation
b)
Expression
c)
Like Term
d)
Constant
124.
Simplify:
3x-5x
a)
2x
b)
8x
c)
-2x
d)
15x2
125.
Simplify:
-3(x - 4)
a)
-3x - 12
b)
3x - 12
c)
3x + 12
d)
-3x + 12
126.
Simplify:
5(2x+5)
a)
10x + 5
b)
10x + 25
c)
7x + 10
d)
7x + 25
127.
Simplify:
-10x + 15 - 3x + 2
a)
13x2 + 17
b)
-13x2 + 13
c)
-13x + 17
d)
-7x + 17
128.
Simplify:
6(–4x – 2) – 2(x + 10)
a)
–26x – 32
b)
–26x + 8
c)
–22x + 8
d)
–26x + 8
129.
Simplify:
4x2 +9x +10 +3x2 +7x +2
a)
23x2+12
b)
35x2
c)
7x2+16x+12
d)
23x+12
130.
What is the first step to solve this equation:
11 - 3x = 44
a)
Add 3 to both sides
b)
Subtract 11 from both sides
c)
Add 11 to both sides
d)
Divide 3 on both sides.
131.
Solve:
x - 8 = -5 
a)
13
b)
-13
c)
3
d)
-3
132.
Solve:
-(n - 8) = -2
a)
6
b)
10
c)
-10
d)
-6
133.
Solve:
7x + 2(x + 3) = -39
a)
x = 8
b)
x = -5
c)
x = 1
d)
x = -2
134.
Solve:
12 + 5w -4w = 15
a)
w=1
b)
w=3
c)
w=5
d)
w=4
135.
Solve:
½(4x - 10) = 11
a)
x = 2
b)
x = 4
c)
x = 6
d)
x = 8
136.
Solve:
52 = -5x - 3
a)
x = 11
b)
x = -11
c)
x = 275
d)
x = -275
137.
Solve:
2x + 3(5x - 7) = 47
a)
1
b)
2
c)
3
d)
4
138.
Multiply
5x(2x + 3)
a)
10x2 + 15x
b)
7x + 15x
c)
7x2 + 8x
d)
25x2
139.
Multiply
(x+3)(x+1)
a)
x2+3x+3
b)
2x+4x+3
c)
x2+4x+3
d)
5x + 3
140.
Multiply
(x+5)2
a)
x2+25
b)
2x+10
c)
x2+10x+25
d)
12x
141.
Classify the polynomial:
3x2 – 8x + 1
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
142.
Classify the polynomial
7x + 1 
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
143.
Which one is NOT a monomial
a)
3x - 4
b)
12z
c)
14v8w
d)
lmnop
144.
What is the degree of the polynomial:
x2 + 2x3 - x
a)
2
b)
3
c)
1
d)
6
145.
What is the degree of the polynomial?
x3 + x6y + y5 + 4x4y4
a)
8
b)
3
c)
7
d)
5
146.
Simplify
(x2 + 7x) + (2x2 - 2x + 3)
a)
3x2 + 5x + 3
b)
5x2 + 3x + 5
c)
2x2 + 5x
d)
3x4 + 5x2 + 5
147.
Simplify
(2x + 5y - z) + (-6x - 4y + 7z)
a)
-4x +6y + 6z
b)
4x + y + 6z
c)
-4x - y + 6z
d)
-4x + y + 6z
148.
Simplify
(3x²-3x+2) - (x²-2x+1)
a)
2x²+x+1
b)
2x²-5x+3
c)
2x²-x+1
d)
4x²-5x+3
149.
Simplify
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3 
b)
-7n2 - 8n + 3 
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
150.
What is the perimeter of the rectangle?
a)
x²+8x-5
b)
2x²+16x-10
c)
2x²+10x-8
d)
6x-2
151.
If the exponents of the variable decrease from left to right, the polynomial is in ____________.
a)
Standard Form
b)
Standard Notation
c)
Simplified
d)
Order
152.
Factor:
6m2 + 16m
a)
2(3m2 + 8m)
b)
2m(3m + 8)
c)
2m(3m - 8m)
d)
not factorable
153.
Factor:
x2 - 14x + 24
a)
(x - 8)(x - 3)
b)
(x - 12)(x - 2)
c)
(x - 6)(x - 4)
d)
(x - 24)(x - 1)
154.
Factor:
x2 - 5x - 24
a)
(x - 8)(x + 3)
b)
(x + 8)(x - 3)
c)
(x - 8)(x - 3)
d)
(x + 8)(x + 3)
155.
Factor:
x2 + 10x + 24
a)
(x + 8)(x + 3)
b)
(x + 6)(x + 4)
c)
(x + 12)(x - 2)
d)
(x + 12)(x + 2)
156.
Factor:
k2-13k+40
a)
(k-10)(k+40)
b)
(k-5)(k-8)
c)
(k+5)(k-8)
d)
(k+10)(k-40)
157.
Factor:
3x2 + 7x + 2
a)
(3x + 2)(x +1)
b)
(3x + 1)(x +2)
c)
(3x + 2)(3x +1)
d)
(3x +1 )(x + 1)
158.
Factor:  
9x2 + 3x - 2
a)
(3x + 1)(3x - 2)
b)
(3x + 2)(3x - 1)
c)
(3x - 1)(3x - 2)
d)
(3x + 2)(3x + 1)
159.
2. Cheryl gets paid $8 per hour for her job at the record store and $15 for working late on Saturday.  She made a total of $96 last week.  Which equation models this situation?
a)
96h + 15 = 8
b)
h/96 = 8
c)
8h + 15 = 96
d)
h/8 = 96
160.

What is the first step in factoring this problem?

x2 + x - 6

a)

Multiply

b)

List the factors of -6

c)

Add the factors of -6

d)

Factor out the GCF

161.

Find the factors of

x2 + x - 6

a)

(x - 6)(x - 9)

b)

(x + 3)(x + 2)

c)

(x + 3)(x - 2)

d)

(x + 2)(x + 4)

162.

Find the factors of

x2 - 5x - 36

a)

(x + 4)(x - 9)

b)

(x - 4)(x + 9)

c)

(x - 9)(x + 6)

d)

(x + 4)(x + 9)

163.

Find the factors of

5m2 - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

164.

Find the factors of

2b2 + 14b - 16

a)

2(b - 1)(b + 8)

b)

6(b - 1)(b - 5)

c)

2(b + 1)(b - 8)

d)

2(b - 1)(b - 8)

165.

Find the factors of

3b2 + 17b + 20

a)

(2b - 5)(b - 7)

b)

(5b - 7)(b - 2)

c)

(b + 5)(3b + 4)

d)

(3b + 5)(b + 4)

166.
8r3 + 16r2
a)
4r2(2r + 4)
b)
8r2(r + 2)
c)
8(r3 + r2)
d)
4(r3 + 2r2)
167.
w3 + 3w
a)
3w(1)
b)
w(w2 + 3)
c)
w3(w + 3)
168.
What is the GCF? 12x+8
a)
12
b)
8
c)
4
d)
x
169.
Factor
5ab2c11 + 2bc5
a)
bc5(5ab2c6 + 2b)
b)
bc5(5abc6 + 2)
c)
b2c5(5bc6 + 2)
d)
c4(5a2b2c7 + 2bc)
170.
Factor the GCF
39y5 + 12y4 - 3y3
a)
3y(13y4 + 4y3 - y2)
b)
3y3(13y2 + 4y - 1)
c)
y3(39y2 + 12y - 3)
d)
not factorable
171.
Factor the GCF
4b5+4b3+16b2
a)
4b3(b4+b2+4b)
b)
4b3(b4+4b+5)
c)
4(b5+b3+4b2)
d)
4b2(b3+b+4)
172.
Factor
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
173.
Factor
4x2-25x+25
a)
4(x-5)(x+5)
b)
(x+5)(4x+5)
c)
(x-5)(4x-5)
d)
(x+2)(9x+1)
174.
a)

x2+4x+8

b)

x2+8x+8

c)

x2+8x+6

d)

x2+6x+8

175.
a)

x2+11x+16

b)

x2+5x+24

c)

x2+11x+24

d)

2x2+11x+24

176.
a)

5x2+16x+8

b)

6x2+12x+8

c)

6x2+16x+6

d)

6x2+16x+8

177.
a)

45x2-26x-8

b)

45x2-26x+8

c)

45x2+26x-8

d)

45x2-46x-8

178.
Find the Product.
(2n + 3)(2n + 1)
a)
4n2 + 8n + 3
b)
4n2 - 8n - 3
c)
4n2 + 8n + 3
d)
4n2 - 8n + 3
179.

Factor: x2−121x^2-121  

a)

(x−11)2\left(x-11\right)^2  

b)

(x+11)(x−11)\left(x+11\right)\left(x-11\right)  

c)

(x−60.5)(x+60.5)\left(x-60.5\right)\left(x+60.5\right)  

d)

(x+11)2\left(x+11\right)^2  

180.

64x2+112x+4964x^2+112x+49  Factor:

a)

(8x−7)(8x+7)\left(8x-7\right)\left(8x+7\right)  

b)

(8x−7)2\left(8x-7\right)^2  

c)

(16x+7)2\left(16x+7\right)^2  

d)

(8x+7)2\left(8x+7\right)^2  

181.

k2−225k^2-225  Factor:

a)

(k +15)(k −15)\left(k\ +15\right)\left(k\ -15\right)  

b)

(k−15)2\left(k-15\right)^2  

c)

(k −25)2\left(k\ -25\right)^2  

d)

(k +10)(k −10)\left(k\ +10\right)\left(k\ -10\right)  

182.

Factor: 49x2−28x+449x^2-28x+4  

a)

(7x+2)(7x−2)\left(7x+2\right)\left(7x-2\right)  

b)

(7x+2)2\left(7x+2\right)^2  

c)

(7x−2)2\left(7x-2\right)^2  

d)

(3.5x−1)2\left(3.5x-1\right)^2  

183.
4x2 - 64y2
a)
Prime
b)
( 2x - 32y) (2 x + 32y) 
c)
( 2x - 8y) (2 x - 8y) 
d)
( 2x - 8y) (2 x + 8y) 
184.
Is this a perfect square trinomial?
x2 + 16x + 64
a)
Yes
b)
No
185.
Is this a perfect square trinomial?
x2 + 18x + 9
a)
Yes
b)
No
186.
Put into standard form: (x - 3)2
a)
x2 + 3x + 9
b)
x2 - 3x - 9
c)
x2 + 6x - 9
d)
x2 - 6x + 9
187.
Put into standard form: (x + 6)2
a)
x2 + 6x + 12
b)
x2 + 6x + 36
c)
x2 + 12x + 6
d)
x2 + 12x + 36
188.
Factor Completely: x4-9x2
a)
x2(x+3)(x-3)
b)
(x2+3x)(x2-3x)
c)
(x2+9)(x-3)(x+3)
d)
x2(x2-9)
189.
Add or Subtract to Simplify:
(5x + x2 - 4) - (4x - x2 + 6)
a)
2x2 + x + 2 
b)
x + 2
c)
2x2 + x - 10 
d)
x - 10 
190.
Simplify the expression.
(4a3 - 8a - 4a2) + (7a3 - 7 - 6a)
a)
11a3 - 4a2 - 14a - 7 
b)
5a3 - 4a2 - 14a - 7 
c)
5a3 - 4a2 - 20a - 7 
d)
5a3 - 9a2 - 20a - 7
191.
(3x3 + 5x - 1) ÷ (x + 1)
a)
3x3 - 3x2 + 8x - 9
b)
3x2 - 3x + 8 - 9/x+1
c)
3x2 + 3x + 8 + 7/x+1
d)
3x3 + 3x2 + 8x + 7
192.

Solve using long division (2x2+6x−20)÷(2x−4)\left(2x^2+6x-20\right)\div\left(2x-4\right)  

a)

x+5+22x−4x+5+\frac{2}{2x-4}  

b)

x−8x-8  

c)

x−5+32x−4x-5+\frac{3}{2x-4}  

d)

x+5x+5   

193.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
194.

Factor Completely:

x2 - 17x + 72

a)

(x - 9)(x + 8)

b)

(x - 9)(x - 8)

c)

x(x - 3)

d)

(x + 9)(x + 8)

195.

Factor Completely:

x2 - 7x - 8

a)

(x + 1)(x - 8)

b)

(x + 1)(x + 8)

c)

5(x + 4)(x + 5)

d)

(x - 1)(x + 8)

196.

Factor Completely:

4k2 + 24k + 36

a)

(2k + 6)2

b)

(2k - 6)2

c)

(2k - 6)(2k + 6)

d)

4(k + 3)2

197.

Factor Completely: 5x2 - 11x + 6

a)

(5x + 6)(x - 1)

b)

(5x - 6)(x - 1)

c)

(2x - 7)(x - 3)

d)

(5x - 6)(x + 1)

198.
What are the factors of
25x2 - 81?
a)
(5x - 9)(5x + 9)
b)
(5x - 9)(5x - 9)
c)
(5x + 9)(5x + 9)
d)
Cannot be factored
199.

A rectangle has an area of 2x2 – 19x +45 ft2. What are the dimensions of the rectangle?

a)

(2x - 9)(x - 5)

b)

(2x + 9)(x + 5)

c)

(2x - 5)(x - 9)

d)

(2x - 5)(x + 9)

200.

Factor:

4x + 6

a)

4(x + 2)

b)

2(2x + 3)

c)

2(2x + 4)

d)

4(x + 2/3)

201.

Which shows the polynomial 8x2+16x+88x^2+16x+8  completely factored?

a)

(4x+4)2\left(4x+4\right)^2  

b)

(4x+4)(2x+2)\left(4x+4\right)\left(2x+2\right)  

c)

8(x+1)28\left(x+1\right)^2  

d)

8(x+1)(x−1)8\left(x+1\right)\left(x-1\right)  

202.

What are the binomial factors of x2+7x−18x^2+7x-18  

(Pick 2 answers)

a)

(x−9)\left(x-9\right)  

b)

(x+9)\left(x+9\right)  

c)

(x−2)\left(x-2\right)  

d)

(x+2)\left(x+2\right)  

203.

If (x−3)\left(x-3\right)  is a factor of  x2+x−12x^2+x-12  , then the other factor is?

a)

(4x−3)\left(4x-3\right)  

b)

(3x−4)\left(3x-4\right)  

c)

(x−4)\left(x-4\right)  

d)

(x+4)\left(x+4\right)  

204.

Written in factored form, the trinomial 2y2+26y+802y^2+26y+80  is equivalent to:

a)

2(y−5)(y−8)2\left(y-5\right)\left(y-8\right)  

b)

(2y+5)(y+8)\left(2y+5\right)\left(y+8\right)  

c)

2(y+5)(y+8)2\left(y+5\right)\left(y+8\right)  

d)

(y+5)(2y+16)\left(y+5\right)\left(2y+16\right)  

205.

When factored completely, x3−9xx^3-9x  is equivalent to:

a)

x(x−3)x\left(x-3\right)  

b)

x(x+3)(x−3)x\left(x+3\right)\left(x-3\right)  

c)

(x+3)(x−3)\left(x+3\right)\left(x-3\right)  

d)

x(x+3)x\left(x+3\right)  

206.

Which expression is the factored form of 2x2−2x−12?2x^2-2x-12?  

a)

2(x+2)(x−3)2\left(x+2\right)\left(x-3\right)  

b)

2(x+6)(x−1)2\left(x+6\right)\left(x-1\right)  

c)

2(x+3)(x−2)2\left(x+3\right)\left(x-2\right)  

d)

2(x+1)(x−6)2\left(x+1\right)\left(x-6\right)  

207.

If (x−3)\left(x-3\right)  and  (x+7)\left(x+7\right)  are the factors of the trinomial  x2+bx−21x^2+bx-21  , what is the value of b?

a)

−3-3  

b)

−4-4  

c)

77  

d)

44  

208.

If (2x−3)\left(2x-3\right)  and  (x+5)\left(x+5\right)  are multiplied to form the trinomial  ax2+bx+cax^2+bx+c  , what is the value of b?

a)

−15-15  

b)

22  

c)

77  

d)

44  

209.

Find the factors of

5m2 - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

210.

Find the factors of

2b2 + 14b - 16

a)

2(b - 1)(b + 8)

b)

6(b - 1)(b - 5)

c)

2(b + 1)(b - 8)

d)

2(b - 1)(b - 8)

211.
Factor by using GCF:
8n3 + 2n2
a)
2n2(4n-1)
b)
2n2(4n + 1)
c)
n2(8n+2)
d)
3n(4n+1)
212.
Factor:
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
213.

Factor out the GCF


3x3 + 9x

a)

3x (x2 + 3)

b)

3x ( x3 + 9)

c)

x (3x2 + 9)

d)

3x (x3 + 3x)

214.
What is the greatest common factor of 20a2b2 and 50b3?
a)
100a2b2
b)
10b3
c)
10ab2
d)
10b2
215.
a)

2x - 5

b)

x - 4

c)

x + 4

d)

2x + 4

216.
Divide: 

(4x2 - 24x + 35) / (2x - 5)
a)
2x - 7
b)
2x - 12
c)
2x + 12
d)
2x + 7
217.

x2 −12x+20x−2\frac{x^{2\ }-12x+20}{x-2}  

a)

x+7

b)

x+2

c)

X-10

d)

X-7

218.

5y2−9y−2y−2\frac{5y^2-9y-2}{y-2}  

a)

5y+1

b)

10y

c)

5y

d)

21

219.
What is the greatest common factor of 20a2b2 and 50b3?
a)
100a2b2
b)
10b3
c)
10ab2
d)
10b2
220.

What is the first step when factoring polynomials?

a)

Find the GCF

b)

List all the terms

c)

Make the X and fill in the top and bottom

d)

Multiply a and c

221.

Factor by grouping:
x3−4x2−4x+16x^3-4x^2-4x+16  

a)

(x+4)(x+2)\left(x+4\right)\left(x+2\right)  

b)

(x−4)(x2−4)\left(x-4\right)\left(x^2-4\right)  

c)

(x+4)(x2−4)\left(x+4\right)\left(x^2-4\right)  

d)

(x−4)(x−2)\left(x-4\right)\left(x-2\right)  

222.

Factor by grouping:

4p3+8p2+3p+64p^3+8p^2+3p+6  

a)

(2p2+3)(p+2)\left(2p^2+3\right)\left(p+2\right)  

b)

(2p2+6)(p+4)\left(2p^2+6\right)\left(p+4\right)  

c)

(4p2+3)(p+2)\left(4p^2+3\right)\left(p+2\right)  

d)

(4p2+8p)(3p+6)\left(4p^2+8p\right)\left(3p+6\right)  

223.

Which of the following would be part of the factored form of  x3−2x2+5x+10x^3-2x^2+5x+10  ?

a)

(x−2)\left(x-2\right)  

b)

(x+2)\left(x+2\right)  

c)

(x2+5)\left(x^2+5\right)  

d)

(x2−5)\left(x^2-5\right)  

224.

 If I were to factor  6n3+3n2+8n+46n^3+3n^2+8n+4  by grouping, my answer would look like  (3n2+4)\left(3n^2+4\right)  times what other binomial?

DO NOT TYPE SPACES

(a)  

225.

What is the factored form of x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)