Free Printable Alg 2 (All): PSTs

1.

Factor the polynomial: $x^2+6x+9$

a)

(x+3)

b)

(x+3)(x+3)

c)

(x+2)(x+3)

d)

Prime (cannot be factored)

2.

Is this a perfect square trinomial?
x² + 16x + 64

a)

Yes

b)

No

3.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

4.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

5.

Which of the following is a perfect square trinomial?

a)

x² – 4x – 4

b)

x² – 6x – 9

c)

x² + 6x – 9

d)

x² – 4x + 4

6.

Put into standard form: (x - 3)²

a)

x² + 3x + 9

b)

x² - 3x - 9

c)

x² + 6x - 9

d)

x² - 6x + 9

7.

Put into standard form: (x + 6)²

a)

x² + 6x + 12

b)

x² + 6x + 36

c)

x² + 12x + 6

d)

x² + 12x + 36

8.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

9.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

10.

Factor

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

11.

Which of the following is a perfect square trinomial?

a)

x² + 14x – 49

b)

x² + 20x + 100

c)

x² – 8x + 4

d)

x² – 5x + 6

12.

Which of the following is NOT a perfect square trinomial?

a)

x² – 16x + 64

b)

x² – 10x + 20

c)

x² – 28x + 196

d)

x² – 24x + 144

13.

Factor: $25x^2-20x+4$

a)

$\left(5x-2\right)^2$

b)

$\left(5x-2\right)^{ }$

c)

Prime (cannot be factored)

d)

(5x+20(5x-2)

14.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

15.

Factor:
18a²-15a

a)

15a(3a-1)

b)

3a(6a-1)

c)

3(6a-5)

d)

3a(6a-5)

16.

Factor Completely: x²-17x+72

a)

(x-9)(x+8)

b)

(x-9)(x-8)

c)

x(x-3)

d)

(x+9)(x+8)

17.

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)

18.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

19.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

20.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

21.

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)

22.

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)

23.

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)

24.

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)

25.

Which of the following is a difference of perfect squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

26.

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

27.

What is the first step when factoring polynomials?

a)

Find the GCF

b)

List all the terms

c)

Make a triangle

d)

Write the answer

28.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

29.

Factor Completely.
8x³ - 18x

a)

2x(4x²-9)

b)

(4x²+3)(2x-3)

c)

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

d)

PRIME

30.

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)

31.

Factor by grouping:
3x³-x²+6x-2

a)

(x²+2)(3x+1)

b)

(x²+2)(3x-1)

c)

(3x³+6x)(x²-2)

d)

none of the aboe

32.

Factor x²-2x-15

a)

(x+5)(x-3)

b)

(x-5)(x-3)

c)

(x-5)(x+3)

d)

(x+5)(x+3)

33.

Factor:
2x² + 13x + 15

a)

(2x + 1)(x + 15)

b)

(x + 3)(x + 5)

c)

(2x - 3)(x - 5)

d)

(2x + 3)(x + 5)

34.

Factor:
2x² -15x + 27

a)

(2x - 9)(x - 3)

b)

(2x + 9)(x + 3)

c)

(2x - 5)(x - 3)

d)

(x - 9)(x - 3)

35.

Factor:
10x² + 9x - 7

a)

(5x + 10)(2x - 7)

b)

(10x + 2)(x - 3)

c)

(5x + 3)(2x + 1)

d)

(5x + 7)(2x - 1)

36.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

37.

x²- 225

a)

( x + 15) ( x + 15)

b)

Prime

c)

( x - 15) ( x + 15)

d)

( x - 15) ( x - 15)

38.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

39.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

40.

4x²- 64y²

a)

Prime

b)

( 2x - 32y) (2 x + 32y)

c)

( 2x - 8y) (2 x - 8y)

d)

( 2x - 8y) (2 x + 8y)

41.

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)

42.

Factor
x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

43.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

44.

Factor: $x^2+10x+25$

a)

(x + 2)(x + 3)

b)

(x - 5)^2

c)

(x + 10)(x - 5)

d)

(x + 5)^2

45.

Factor: $x^2-8x+16$

a)

(x - 2)(x - 8)

b)

(x + 4)(x - 4)

c)

(x - 4)(x + 4)

d)

(x - 4)(x-4)

46.

Factor: $x^2-14x+49$

a)

(x + 7)(x - 7)

b)

(x - 7)(x-7)

c)

(x - 14)(x - 7)

d)

(x - 7)(x + 7)

47.

#17 Factor: $x^2+12x+36$

a)

(x + 6)^2

b)

(x + 2)(x + 18)

c)

(x-6)^2

d)

(x + 4)(x + 9)

48.

18) Factor: $x^2-16x+64$

a)

(x + 8)^2

b)

(x - 8)^2

c)

(x - 10)(x - 6)

d)

(x - 4)(x - 4)

49.

19) Factor: $-4x^2-24x-36$

a)

-4(x + 6)(x + 3)

b)

-4(x - 3)(x + 4)

c)

-4(x + 2)(x + 9)

d)

-4(x + 3)^2

50.

Which of the following expressions is a factor of this polynomial?

a)

(n + 3)

b)

(5n + 2)

c)

(5n - 1)

d)

(n - 2)

51.

Which expression is a factor of $n^2+3n−54?$

a)

n − 9

b)

$n^2+9$

c)

n + 9

d)

n + 6

52.

What are the length and width of the rectangle?

a)

$4x-3$ & $x-5$

b)

$4x+3$ & $x-5$

c)

$x+3$ & $4x-5$

d)

$x-3$ & $4x-5$

53.

Which of the following is a difference of perfect squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

54.

Factor.

18x² - 50

a)

2 ( 9x² - 25 )

b)

( 3x + 5 ) ( 3x - 5 )

c)

2 ( 3x + 5 ) ( 3x - 5 )

d)

2 ( 3x - 5 ) ( 3x - 5 )

55.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

56.

Factor

Rewrite this Sum as a Product

r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

57.

What is the Greatest Common Factor of 10 and 5?

(a)

58.

Which of the following do you think is the GCF of

$12x^3+3x^2$

a)

$3x$

b)

3

c)

$3x^2$

d)

$x^2$

59.

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

60.

Factor
x³ - 125

a)

(x + 5) (x - 5)

b)

(x - 5)(x² + 5x + 25)

c)

(x - 5)(x² - 5x + 25)

d)

(x - 5)³

61.

Factor completely:

$30x^3-90x^2-80x$

a)

$10x\left(3x^2-9x-8\right)$

b)

$x\left(30x^2-90x-80\right)$

c)

$10\left(3x^3-9x^2-8x\right)$

d)

$10x\left(-14x^3\right)$

62.

Which expression is a factor of $121x^2-36$ ?

a)

11x+6

b)

11x+12

c)

11x-36

d)

121x-6

63.

Factor the following expression:

$k^4-36$

a)

$\left(k^2-6\right)\left(k^2+6\right)$

b)

$\left(k^4-6\right)\left(k^4+6\right)$

c)

(k-6)(k+6)

d)

Prime

64.

7k² + 9k

a)

k(7k - 9)

b)

k(7k + 9)

c)

7k(k + 9)

d)

(k+3)(7k + 3)

65.

Factor out the GCF

18x³ + 81x - 27

a)

9x (2x² + 9x - 3)

b)

3 (6x³ + 27x - 9)

c)

9 (2x³ + 9x - 3)

d)

9 (2x² + 9x - 3)

66.

What do you call a polynomial that cannot be factored?

a)

FOIL

b)

Prime

c)

Simplified

d)

Proper

67.

Factor:
4n⁶+16n⁴-8n

a)

4n(n⁴+4n³-2)

b)

4n(n⁵+4n³-2)

c)

12n(n⁵+4n⁴-2)

d)

16n(n⁵+4n³-2)

68.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

69.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

70.

Is this a perfect square trinomial?
x² + 16x + 64

a)

Yes

b)

No

71.

Which of the following is a perfect square trinomial?

a)

x² + 14x – 49

b)

x² + 20x + 100

c)

x² – 8x + 4

d)

x² – 5x + 6

72.

Which of the following is a perfect square trinomial?

a)

$x^2+5x-25$

b)

$x^2-10x+100$

c)

$x^2-5x+100$

d)

$x^2-10x+25$

73.

Given the perfect square trinomial, identify the equivalent expression

x²+14x+49

a)

(x+14)²

b)

(x+49)²

c)

(x-7)²

d)

(x+7)²

74.

What value of c makes x² + 24x + c a perfect square trinomial?

a)

576

b)

144

c)

24

d)

12

75.

Which of the following is a perfect square trinomial?

a)

5x² – 4x +4

b)

25x² + 6x +8

c)

7x² – 6x –+9

d)

25x² – 20x + 4

76.

Which of the following is a perfect square trinomial?

a)

x² – 18x + 81

b)

x² – 12x + 6

c)

x² + 20x + 40

d)

x² – 12x – 36

77.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

78.

Factor completely:
3x² - 12x + 12

a)

3(x - 2)(x - 2)

b)

3(x - 2)(x + 2)

c)

3(x - 1)(x - 4)

d)

3(x - 3)(x - 1)

79.

Factor:
4y² - 9

a)

(2y - 3)(2y + 3)

b)

(4y - 3)(y + 3)

c)

(2y - 9)(2y + 1)

d)

Prime

80.

Put into standard form: (x + 5)²

a)

x² + 10x + 25

b)

x² + 5x + 25

c)

x² + 25

d)

x² + 10x + 5

81.

Simplify (-8v⁴ + 4v³ + 3v) + (- 8v⁴+ 4v - 7)

a)

-17v⁴ + 4v³ + 2v - 7

b)

-16v⁴ + 4v³ + 10v - 7

c)

-16v⁴ + 4v³ + 7v - 7

d)

-16v⁴ + 4v³ + 2v - 7

82.

Combine (3x - 4) + (12x + 10)

a)

x - 12

b)

15x + 6

c)

36x + 40

d)

17x + 9,000

83.

Simplify (9x + 17) + (19x - 27)

a)

28x + 44

b)

28x - 10

c)

-28x + 10

d)

-171x - 459

84.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

85.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

86.

Classify by number of terms:
9x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

87.

What is the standard form of the polynomial,
7x - 125 - 6x⁴ + 14x²

a)

125 + 7x - 14x² +6x⁴

b)

6x⁴ -14x² - 7x +125

c)

125 + 14x² + 7x - 6x⁴

d)

-6x⁴+ 14x² + 7x - 125

88.

Every polynomial isn't a monomial, but every monomial is a polynomial

a)

True

b)

False

89.

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

90.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

91.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

92.

Label the polynomial

x^2\ -\ 4x\ +\ 8

a)

monomial

b)

trinomial

c)

binomial

d)

none of these

93.

The length of a rectangle is x - 5. The width is x + 1. What is the area?

a)

$x^2\ -\ 4x\ -\ 5$

b)

$2x\ -\ 4$

c)

$x^2\ +\ 6x\ -\ 5$

d)

none of these

94.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

95.

(x + 7)(x - 2)

a)

x² - 5x + 5

b)

x²- 9x - 14

c)

x² - 5x - 14

d)

x² + 5x - 14

96.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

97.

Multiply: 2x(-2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

98.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

99.

$\left(x+4\right)\left(x-6\right)\left(x-5\right)$

a)

$x^3-7x^2-14x+120$

b)

$x^4-7x^3-14x^2+120x$

c)

$-x^3+7x^2+14x+120$

d)

$-x^3-7x^2-14x-120$

100.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

101.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

102.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

103.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

104.

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

$6y^2\ +3y^2\ -4y^2$

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

105.

$\frac{-12a^{4\ }+\ 6a^3}{6a^3}$

a)

$2a$

b)

$-2a+1$

c)

$2a\ +1$

d)

$-2a\ +\ 1a$

106.

5x²(2x - 3)

a)

5x² + 2x - 3

b)

10x³ - 15x²

c)

-5x2

d)

7x³ - 15x²

107.

Combine Like Terms:
4y + 3x³ + 2y + 8x³ - 6y

a)

11x³

b)

11x³ + 12y

c)

5x³

d)

11x⁶

108.

Divide

$\frac{10x^8y^5}{4x^2y^5}$

a)

$6x^6y$

b)

$\frac{5x^6}{2}$

c)

$\frac{5x^6y}{2}$

d)

$6x^6$

109.

Divide

$\frac{\text{3}x^2-2xy}{\text{2x}}$

a)

$1.5x^{3\ }-x^2y$

b)

$1.5x\ -\ y$

c)

$1.5x\ +\ y$

d)

$1.5x\ -\ 2y$

110.

Divide

$\frac{15x^9-40x^6}{5x^3}$

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

111.

Divide

$\frac{-20p^2-16p}{-4p}$

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

112.

Divide

$\frac{-12a^{4\ }+\ 6a^3}{6a^3}$

a)

$2a$

b)

$-2a+1$

c)

$2a\ +1$

d)

$-2a\ +\ 1a$

113.

Divide

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

$6y^2\ +3y^2\ -4y^2$

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

114.

x⁴- 10x³+ 35x²- 50x + 24 ÷ x² - 3x + 2

a)

x² - 7x + 12

b)

x³+ 3x² + 4x - 1

c)

x² - 1

d)

x² + 7x - 12

115.

Divide

$\frac{10x^8y^5}{4x^2y^5}$

a)

$6x^6y$

b)

$\frac{5x^6}{2}$

c)

$\frac{5x^6y}{2}$

d)

$6x^6$

116.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

117.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

118.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

119.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

120.

(-2)³⋅(-2)⁶

a)

(-2)⁹

b)

(-2)¹⁸

c)

(-2)⁻³

d)

(-2)

121.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

122.

x⁵⁄x³

a)

x²

b)

x

c)

1

d)

x⁸

123.

Simplify the expression.

a)

1

b)

g¹⁰

c)

g²⁵

d)

g

124.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

125.

Simplify using the exponent properties $\frac{21d^6r^3}{7d^{12}r^4}$

a)

$3d^{-6}r^{-1}$

b)

$3d^{18}r^7$

c)

$3d^6r^1$

d)

$\frac{1}{3d^{-6}r^{-1}}$

126.

a)

b)

2x²z⁴

c)

3x²y⁵z⁴

d)

127.

a)

$\frac{16x^{16}z^{32}}{y^{28}}$

b)

$\frac{-16x^{16}z^{32}}{y^{28}}$

c)

$\frac{x^{16}z^{32}}{16y^{28}}$

d)

$-8x^{-8}y^3z^{-12}$

128.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

129.

Factor: $x^2-10x+25$

a)

(x - 5)(x - 5)

b)

(x - 5)(x + 5)

c)

(x - 10)(x + 5)

d)

(x - 2)(x - 12)

130.

Factor: $x^2+4x+4$

a)

(x + 2)(x + 2)

b)

(x + 4)(x + 4)

c)

(x + 2)(x - 2)

d)

(x + 1)(x + 4)

131.

30) Factor: $25x^2+10x\left(y^2+5\right)+\left(y^2+5\right)^2$

a)

(5x + y^2 - 5)^2

b)

(5x - y^2 + 5)^2

c)

(5x + 2y^2 + 5)^2

d)

(5x + y^2 + 5)^2

132.

29) $4x^2+4x\left(5y-3\right)+\left(5y-3\right)^2$ Factor:

a)

(4x + 5y - 3)(x + 5y - 3)

b)

(2x + 3y - 5)(2x + 3y + 5)

c)

(2x - 5y + 3)^2

d)

(2x + 5y - 3)^2

Alg 2 (All): PSTs

Total questions: 132

Worksheet time: 33hrs 31mins

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