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Polynomials Concepts

Total questions: 26

Worksheet time: 27mins

Name
Class
Date
1.

What is the y-intercept of x2 + 2x + 1?

a)

1

b)

2

c)

3

d)

4

2.

What is the degree of x2 + 3x3 - x4?

a)

2

b)

3

c)

4

d)

5

3.
What is the degree of x(x + 2)(x - 3)?
a)
1
b)
2
c)
3
d)
4
4.

What is the degree of (x + 2)(x - 1)(x + 3)(x - 2)2?

a)

2

b)

3

c)

4

d)

5

5.

What is a possible degree of the graphed polynomial?

a)

2

b)

3

c)

4

d)

5

6.

What is a possible degree of the graphed polynomial?

a)

2

b)

3

c)

4

d)

5

7.

What is the degree of the graphed polynomial?

a)

2

b)

3

c)

4

d)

5

8.
Which of the following is a zero of (x + 2)(x - 1)?
a)
2
b)
1
c)
-1
d)
0
9.
Which of the following is a zero of x(x + 4)(x - 2)
a)
0
b)
4
c)
-2
d)
1
10.
Which of the following is a zero of (3 - x)(x - 2)(x - 1)?
a)
3
b)
-1
c)
-3
d)
0
11.

Which zero will "bounce" off of the x-axis (or make a parabolic shape) for x2(x - 1)(x + 2)(x + 3)

a)

0

b)

1

c)

-2

d)

-3

12.
Which zero(s) will "bounce" off the x-axis for (x + 1)(x - 2)2(x+ 3)(x + 1)
a)
2
b)
2 and -1
c)
-1
d)
2 and -3
13.

What is the end behavior of a second degree polynomial with a positive leading coefficient?

a)

As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more positive.

b)

As x gets larger and larger in the negative direction, f(x) gets more negative. As x gets larger and larger in the negative direction, f(x) gets more positive.

c)

As x gets larger and larger in the positive direction, f(x) gets more negative. As x gets larger and larger in the negative direction, f(x) gets more positive.

d)

As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more negative.

14.
What is the end behavior of a fourth degree polynomial with a negative leading coefficient?
a)
up, up
b)
down, down
c)
down, up
d)
up, down
15.
What is the end behavior of a fifth degree polynomial with a negative leading coefficient?
a)
up, up
b)
down, down
c)
down, up
d)
up, down
16.
For the pictured polynomial, at which interval is it increasing?
a)
(0, 2)
b)
(2, 3.5)
c)
(3.5, ∞)
d)
(2,4)
17.

How many relative maximums does the polynomial function have?

a)

2

b)

1

c)

3

d)

none

18.

What is the constant of x(x + 2)(x - 3)?

a)

1

b)

2

c)

3

d)

4

e)

0

19.

Which factor has a multiplicity of 2 of (x + 2)(x - 1)(x + 3)(x - 2)2? What does this tell you about the graph?

a)

(x + 2), and it will go straight through the x-intercept

b)

(x - 1), and it will make a parabola shape at the x-intercept.

c)

(x +3), and it will go straight through the x-intercept.

d)

(x - 2), and it will make a parabola shape at the x-intercept.

20.

What is the end behavior of a third degree polynomial with a positive leading coefficient?

a)

As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more positive.

b)

As x gets larger and larger in the negative direction, f(x) gets more negative. As x gets larger and larger in the negative direction, f(x) gets more positive.

c)

As x gets larger and larger in the positive direction, f(x) gets more negative. As x gets larger and larger in the negative direction, f(x) gets more positive.

d)

As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more negative.

21.

How many relative minimums does the polynomial function have?

a)

2

b)

1

c)

3

d)

none

22.

What is the end behavior of a fourth degree polynomial with a negative leading coefficient?

a)

As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more positive.

b)

As x gets larger and larger in the negative direction, f(x) gets more negative. As x gets larger and larger in the negative direction, f(x) gets more negative.

c)

As x gets larger and larger in the positive direction, f(x) gets more negative. As x gets larger and larger in the negative direction, f(x) gets more positive.

d)

As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more negative.

23.
What is the end behavior for
f(x)=2x2+x
a)
A
b)
B
c)
C
d)
D
24.
What is the end behavior for
f(x)= -x3+2x+1
a)
A
b)
B
c)
C
d)
D
25.
What is the end behavior for
f(x)= x+x4
a)
A
b)
B
c)
C
d)
D
26.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd