Free Printable Algebra 2: Unit 2B Review

1.

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

a)

5

b)

4

c)

3

d)

2

2.

a)

p(x) = (x − 1)(x + 2)(x + 5)

b)

p(x) = (x + 1)(x − 2)²(x − 5)

c)

p(x) = (x − 1)²(x + 2)(x + 5)

d)

p(x) = (x − 1)(x + 2)²(x + 5)

3.

a)

A

b)

B

c)

C

d)

D

4.

a)

x = −3, x = 2

b)

x = −3, x = 0, x = 2

c)

x = 0

d)

x = −2, x = 0, x = 3

5.

a)

f(x) = (x − 1)²(x + 2)(x + 4)³

b)

f(x) = (x + 1)(x − 2)(x − 4)

c)

f(x) = (x + 1)²(x − 2)(x − 4)³

d)

f(x) = (x + 1)(x − 2)(x − 4)³

6.

a)

2

b)

1

c)

4

d)

None

7.

a)

4

b)

1

c)

2

d)

5

8.

a)

The function is Odd

b)

The function is Even

c)

The function has 5 real zeros

d)

The function is Positive

9.

a)

The function is Odd, Positive

b)

The function has 1 complex root

c)

The function has 2complex roots

d)

The function is Odd, Negative

10.

a)

The function is Even, Positive

b)

The function is Even, Negative

c)

The function is Odd, Negative

d)

The function is Odd, Positive

11.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

a)

A

b)

B

c)

C

d)

D

14.

a)

A

b)

B

c)

C

d)

D

15.

What are the solution(s) for the polynomial $f\left(x\right)=x^3+6x^2+13x$

a)

$\left[0,-3+i\sqrt{2},-3-i\sqrt{2}\right]$

b)

$\left[0,-4+\sqrt{3},-4-\sqrt{3}\right]$

c)

$\left[0,-2+3i,-2-3i\right]$

d)

$\left[0,-3+2i,-3-2i\right]$

16.

What are the roots for the polynomial $f\left(x\right)=x^3-5x^2-4x+20$

a)

$\left[5,2,-1\right]$

b)

$\left[\frac{5}{2},1,-2\right]$

c)

$\left[5,2,-4\right]$

d)

$\left[5,2,-2\right]$

17.

What are the x-intercept(s) of the polynomial $f\left(x\right)=3x^5-4x^3+x$

a)

$\left[0,1,-\frac{1}{3},\frac{\sqrt{3}}{3},-\frac{\sqrt{3}}{3}\right]$

b)

$\left[0,1,-3,\frac{\sqrt{3}}{3},-\frac{\sqrt{3}}{3}\right]$

c)

$\left[0,1,-1,\frac{\sqrt{5}}{5},-\frac{\sqrt{5}}{5}\right]$

d)

$\left[0,1,-1,\frac{\sqrt{3}}{3},-\frac{\sqrt{3}}{3}\right]$

18.

What are the zero(s) for the polynomial $f\left(x\right)=2x^5-13x^3+20x$

a)

$\left[0,\ \frac{\sqrt{10}}{2},-\frac{\sqrt{10}}{2},2,-\frac{2}{3}\right]$

b)

$\left[0,\frac{i\sqrt{14}}{2},-\frac{i\sqrt{14}}{2},2,-2\right]$

c)

$\left[0,\frac{\sqrt{10}}{2},-\frac{\sqrt{10}}{2},2,-2\right]$

d)

$\left[0,i\sqrt{3},-i\sqrt{3},2,-2\right]$

19.

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

a)

10x²

b)

18x² + 4

c)

6x² + 4

d)

3x² + 4

20.

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

21.

p(x) = 4x - 5
q(x) = 2x²
Find p(q(x))

a)

8x² + 5

b)

8x² - 10x

c)

8x² - 5

d)

None of these.

22.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(x))

a)

3x + 8

b)

3x - 2

c)

3x + 4

d)

None of these.

23.

p(x) = 3x + 4
q(x) = 2x²
Find p(p(-3))

a)

-9

b)

7

c)

-11

d)

None of these

24.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

25.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

26.

f(x) = x² + x
g(x) = 3x + 1
find the value of f(g(4))

a)

182

b)

40

c)

61

d)

None of the Above

27.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(x))

a)

6x² + 4

b)

18x²+ 48x + 32

c)

18x² + 32

d)

None of these.

28.

Given that
f(x) = x² + x
and
g(x) = 3x + 1,
find the value of g(f(-2)).

a)

-14

b)

20

c)

6

d)

7

29.

a)

A

b)

B

c)

C

d)

D

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

A

b)

B

c)

C

d)

D

32.

Given f and g in the graph,

what is f(g(2)) ?

a)

3

b)

8

c)

1

d)

4

33.

Given f and g in the graph,

what is f(f(3)) ?

a)

3

b)

2

c)

4

d)

1

34.

find h(f(-1))

a)

-5

b)

4

c)

-4

d)

12

35.

Find g(f(-2))

a)

-18

b)

-2

c)

1

d)

9

36.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

37.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

a)

A

b)

B

c)

C

d)

D

Algebra 2: Unit 2B Review

Total questions: 40

Worksheet time: 7hrs 16mins

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