Free Printable Alg 2 Quiz Review 4.1

1.

Classify by degree of polynomial:
3x² – 8x + 1

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

2.

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

3.

a)

(-2.55, 0), (2.55, 0)

b)

(-3, 0), (-2, 0), (2, 0), (3, 0)

c)

(0, 36)

d)

(0, -3), (0, -2), (0, 2), (0, 3)

4.

In the above graph, which root has a multiplicity of 2?

a)

-1

b)

-3

c)

-120

d)

4

5.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

6.

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

a)

As x approaches $\pm\infty$ , f(x) approaches - $\infty$ .

b)

As x approaches $\pm\infty$ , f(x) approaches $\infty$ .

c)

As f(x) approaches $\pm\infty$ , x approaches $\infty$ .

d)

As f(x) approaches $\pm\infty$ , x approaches - $\infty$ .

7.

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

8.

The domain of a polynomial function is always (-∞, +∞).

a)

True

b)

False

9.

What is the factored form of a function if it has zeros of 2, 3 and -1?

a)

f(x) = (x-2)(x-3)(x+1)

b)

f(x) = (x-1)(x-2)(x-3)

c)

f(x) = (x-1)(x+2)(x+3)

d)

f(x) = (x+1)(x+2)(x+3)

10.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

11.

What is the leading coefficient?

a)

Positive

b)

Negative

12.

f(x)=(x+4)(x-3)(x-2)

List the zeros for this function.

a)

x=-4, x=3, x=-2

b)

x=-4, x=3, x=2

c)

x=-4, x=3, x=-2

d)

x=4, x=3, x=2

13.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

14.

If a zero of a polynomial function has multiplicity 3 that means:

a)

The x intercept is at (4, 0)

b)

The graph will "bounce back" at that zero

c)

The graph will "pass through" at that zero

d)

Zeros cannot have multiplicity of 4

15.

Describe the end behavior of
f(x) = 2x² + 6x⁵ + 10x

a)

As x approaches $\pm\infty$ , f(x) approaches $\infty$ .

b)

As x approaches $\pm\infty$ , f(x) approaches - $\infty$

c)

As f(x) approaches $\pm\infty$ , x approaches $\infty$

d)

As f(x) approaches $\pm\infty$ , x approaches - $\infty$

16.

Which of the following allows you to describe the end behavior of a polynomial?

a)

the degree and the constant

b)

the leading coefficient and the constant

c)

degree and the variable

d)

the degree and the leading coefficent

17.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

18.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

19.

If the graph of a function touches the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

20.

What are the x-intercepts of
f(x)=(x - 10)(x + 10)

a)

10

b)

(10 , 0) and (-10 , 0)

c)

(0, -10) and (0, 10)

d)

0

21.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

22.

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

23.

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

24.

(4x³-5x²+3x)+(-2x³-x²+6x)

a)

2x³-6x²-9x

b)

2x³+6x²+9x

c)

-2x³-6x²+9x

d)

2x³-6x²+9x

25.

Multiply
(4x+3)(2x-1)

a)

8x²-2x-3

b)

8x-3

c)

8x²+6x-3

d)

8x²+2x-3

26.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

27.

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

a)

-17v⁴ + 4v³ + 2v - 7

b)

-16v⁴ + 4v³ + 10v - 7

c)

-16v⁴ + 4v³ + 7v - 7

d)

-16v⁴ + 4v³ + 2v - 7

28.

Find the area of a rectangle with length (x-5) and width (3x+1).

a)

3x²+16x-5

b)

3x²-14x+5

c)

3x²-14x-5

29.

(2x + 3)(3x + 4)

a)

6x² + 17x + 7

b)

6x² + 17x + 12

c)

6x² + 8x + 12

d)

6x² + 9x + 12

30.

(4x + 3)(x + 2)

a)

x² + 11x + 6

b)

4x² + 8x + 6

c)

4x² + 3x + 6

d)

4x² + 11x + 6

31.

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

a)

6x² + 17 + 5

b)

6x + 17x + 5

c)

6x² + 17x + 5

d)

6x² + 17 + 5x

32.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

33.

Using Pascal's Triangle simplify: (x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

34.

(3x - 5)(4x² - 2x - 3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

35.

Add or Subtract to Simplify:
(x + 2x²) + (4x² + 7x)

a)

6x² + 8x

b)

8x² + 6x

c)

2x² + 6x

d)

2x² + 8x

36.

Add or Subtract to Simplify:
(4x - 2x³) + (5x³ - 4x + 5)

a)

3x³ + 5

b)

3x³ + 8x + 5

c)

3x² + 5

d)

7x³ + 8x + 5

37.

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

38.

Add or Subtract to Simplify:
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

39.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

40.

Add: (3x² + 2x + 1) + (2x² - 4x - 5) + (3x - 1)

a)

5x² + 6x - 7

b)

8x²- 3x - 5

c)

5x²+ x - 5

d)

6x² + 8x + 5

41.

Divide:
(6x + 9) / (3x)

a)

2 + 9/3x

b)

2 + 9

c)

2 + 9/3

d)

2

42.

Divide:
(24x + 4) / (6x+1)

a)

4

b)

4 + 4/6x+1

c)

4x + 0

d)

4x

43.

Divide:
(9x² + 6) / (3x)

a)

3x + 6/3x

b)

3x + 2

c)

3 + 6/3x

d)

3x + 6

44.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

45.

Find the product:
(y - 3)(y + 7)

a)

y² - 21

b)

y² + 10y - 21

c)

y² + 4y - 21

d)

2y - 10

46.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

47.

Simplify
(p − 8)²
Hint: (p − 8)² = (p − 8)(p − 8)

a)

p ² − 16p − 64

b)

p ² + 16p + 64

c)

p ² − 16p − 8

d)

p ² − 16p + 64

48.

What type of polynomial is
4x² - 21x + 5

a)

Monomial

b)

Binomial

c)

Trinomial

49.

What type of polynomial is
4x³+ 2

a)

Monomial

b)

Binomial

c)

Trinomial

50.

What type of polynomial is
2x²

a)

Monomial

b)

Binomial

c)

Trinomial

51.

What is the degree of the following polynomial?
2x³

a)

First Degree

b)

Second Degree

c)

Third Degree

d)

Fourth Degree

52.

What is the degree of the following polynomial?
3x⁴ + 4x + 1

a)

First Degree

b)

Second Degree

c)

Third Degree

d)

Fourth Degree

53.

which binomial product would produce this as an answer?
x² - 100

a)

(x - 10)(x +10)

b)

(x - 2)(x + 50)

c)

(x - 4)(x + 25)

d)

(x - 1)(x + 100)

54.

Remember to combine like terms
CLICK THIS TO HIDE TEXT

a)

A

b)

B

c)

C

d)

D

55.

Remember to combine like terms
CLICK THIS TO HIDE TEXT

a)

A

b)

B

c)

C

d)

D

56.

Remember to combine like terms
CLICK THIS TO HIDE TEXT

a)

A

b)

B

c)

C

d)

D

57.

Remember to combine like terms
CLICK THIS TO HIDE TEXT

a)

A

b)

B

c)

C

d)

D

58.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

59.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

60.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

61.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

62.

Find the quotient when (21x²- 52x + 32) is divided by (7x - 8).

a)

3x + 4

b)

3x + 3

c)

3x - 4

d)

3x + 2

63.

The area of a rectangular pool table is: x² + 14x +40.

The length is x + 4. What is the width?

a)

x + 8

b)

x + 14

c)

x + 10

d)

x +4

64.

Divide:
(24x + 4) / (6x+1)

a)

4

b)

4 + 4/6x+1

c)

4x + 0

d)

4x

65.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

66.

$\frac{6x^2+19x+3}{x+3}$

(a)

67.

$\frac{15x^2+19x+6}{5x+3}$

(a)

68.

$\frac{5x^2-9x-2}{x-2}$

(a)

69.

$\frac{81x^9-54x^6+27x^3}{9x}$

a)

$9x^9-6x^6+3x^3$

b)

$9x^8-6x^5+3x^2$

c)

$9x^{10}-6x^7+3x^4$

d)

$81x^8-6x^5+3x^2$

70.

$\frac{36x^2-121}{6x+11}$

(a)

71.

$\frac{4x^2-17x+18}{x-2}$

(a)

72.

$\frac{14x^2+17x-22}{14x-11}$

(a)

73.

$\frac{75x^8+50x^4+30x^3+5x^2}{5x^2}$

a)

$15x^8+10x^4+6x^3+x^2$

b)

$15x^6+10x^2+6x$

c)

$15x^{10}+10x^6+6x^5+x^4$

d)

$15x^6+10x^2+6x+1$

74.

$\frac{x^2-16}{x-4}$

(a)

75.

$\frac{x^2+2x-48}{x-6}$

(a)

76.

$\frac{x^2+14x+13}{x+1}$

(a)

77.

$\frac{16x^8+24x^6-40x^4}{4x^3}$

a)

$4x^5+6x^3-10x$

b)

$4x^8+6x^6-10x^4$

c)

$12x^5+20x^3-44x$

d)

$4x^{11}+6x^9-10x^7$

78.

$\frac{x^2+10x+25}{x+5}$

(a)

79.

$\frac{4x^2-4x+1}{2x-1}$

(a)

80.

Factor by using GCF:

8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

81.

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)

82.

Factor the Trinomial:

x² - 17x + 72

a)

(x - 9)(x + 8)

b)

(x - 9)(x - 8)

c)

x(x - 3)

d)

(x + 9)(x + 8)

83.

What is the GCF of 28ab and 42b?

a)

4b

b)

6b

c)

7b

d)

14b

84.

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 above

85.

Factor the Trinomial:

3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

86.

Factor by using GCF:

3x³+ 9x²- 15x

a)

x(3x² + 9x - 15)

b)

3x(x² + 3x - 5)

c)

3x(x² - 9x + 15)

d)

x(3x² -9x + 15)

87.

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)

88.

Factor the Trinomial:

3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

89.

Factor by using GCF:

4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

90.

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)

91.

Factor the Trinomial:

9x²-6x-8

a)

(3x+2)(3x-4)

b)

(3x+2)(3x+4)

c)

(3x-2)(3x-4)

d)

(x-1)(9x+8)

92.

Factor by using GCF:

8r³ + 16r²

a)

4r²(2r + 4)

b)

8r²(r + 2)

c)

8(r³ + r²)

d)

4(r³ + 2r²)

93.

Factor by Grouping:

4y³+ y + 12y²+ 3

a)

4y²(y + 3) + 3

b)

4y³+ 12y²+ y + 3

c)

(4y² + 1)(y + 3)

94.

Factor the Trinomial:

5x² + 17x + 6

a)

(5x + 3)(x + 2)

b)

(5x + 2)(x + 3)

c)

(5x + 1)(x + 6)

d)

(5x + 6)(x + 1)

95.

Factor by using GCF:

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

Prime

96.

Factor by Grouping:

p⁴- 3p³ - 16p² + 48p

a)

p² ( p - 3) (p - 3)

b)

(p³ - 16) (p - 3)

c)

(p + 4) (p - 4) (p - 3)

d)

(p³ - 16p) (p - 3)

97.

Factor the Trinomial:

2m² + 3m - 9

a)

2(m + 3)(m - 3)

b)

(2m - 3)²

c)

(m + 3)(2m - 3)

d)

(2m + 3)(m - 3)

98.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

99.

Complete the formula

a³+b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

100.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

101.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

102.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

103.

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)

104.

Factor using differencesum/ of cubes. (use your notes!)
a³ + b³

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

105.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

106.

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

a)

No

b)

Yes

c)

Yes, getting GCF first

d)

It is a sum of squares

107.

WHAT FACTORING TECHNIQUE YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF 27X³-343?

a)

DIFFERENCE OF TWO CUBES

b)

DIFFERENCE OF TWO SQUARES

c)

FACTORING BY GCF

d)

SUM OF TWO CUBES

108.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

109.

x⁴- 16

a)

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

b)

( x² - 4) ( x² + 4)

c)

( x² - 8) ( x² + 8)

d)

( x - 4) ( x + 4)

110.

x²- 225

a)

( x + 15) ( x + 15)

b)

Unfactorable

c)

( x - 15) ( x + 15)

d)

( x - 15) ( x - 15)

111.

x⁶- 400

a)

( x³ - 200) ( x³ + 200)

b)

( x² + 20) ( x² + 20)

c)

( x - 20) ( x + 20)

d)

( x³ - 20) ( x³ + 20)

112.

4x²- 64y²

a)

Unfactorable

b)

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

c)

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

d)

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

113.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Unfactorable

114.

x²+ 81

a)

Unfactorable

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

115.

Factor the Polynomial:

121r² - 64t²

a)

(11r + 8t)(11r - 8t)

b)

(11r - 8t)(11r - 8t)

c)

(11r + 8t)(11r + 8t)

d)

Unfactorable

116.

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)

117.

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)

118.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

119.

Fully Factor the Following

16x²+25

a)

Unfactorable

b)

(4x-5)(4x+5)

c)

(4x+5)(4x-5)

d)

(4x+5)²

Alg 2 Quiz Review 4.1 - 4.4

Total questions: 119

Worksheet time: 6hrs 19mins

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