Free Printable Study Guide- Intro to Polynomials

1.

Match each polynomial to its factored form:

a)

$x^2+5x+4$

1.

(x+4)(x+1)

b)

$x^2-5x+4$

2.

(x-4)(x-1)

c)

$x^2+3x-4$

3.

(x+4)(x-1)

d)

$x^2-3x-4$

4.

(x-4)(x+1)

2.

Match the following functions with their zeros and multiplicities.

a)

$f\left(x\right)=\left(x-3\right)^2\left(x+1\right)$

1.

x=3 multi 2 touch,
x=-1 multi 1 cross

b)

$f\left(x\right)=\left(x-3\right)\left(x+1\right)$

2.

x=3 multi 1 cross,
x=-1 multi 1 cross

c)

$f\left(x\right)=x\left(x+3\right)^2\left(x+1\right)^2$

3.

x=0 multi 1,
x=-3 multi 2 ,
x=-1 multi 1

d)

$f\left(x\right)=x^2\left(x-3\right)^2\left(x-1\right)$

4.

x=0 multi 2,
x=3 multi 2

x=1 multi 1

e)

$f\left(x\right)=\left(x-3\right)\left(x+1\right)^2$

5.

x=3 multi 1 cross,

x=-1 multi 2 touch

3.

What are the zeros?

a)

x= -4, 3, 4

b)

x= -4, -4, 3, 4

c)

x = -4, 3

d)

x= -4, -4, 3, 3

4.

What is another name for an x-intercept?

a)

Parabola/Quadratic

b)

Root/Zeros

c)

Asymptotes/Zeros

d)

Quadratic/Root

5.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

cross cross cross

b)

6, -5

cross cross

c)

0, -6, 5

cross cross cross

d)

1, -6, 5

cross cross cross

6.

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

7.

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)

8.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 with Degree: 7

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

9.

Please select the solution that describes if zeros crosses or turns at the x-axis for each x-intercept.

a)

2 crosses, 1 crosses, -3 turns, -4 turns

b)

1 crosses, -3 turns, - 4 crosses

c)

1 crosses, -3 turns, -4 turns

d)

1 turns, -3 crosses, -4 crosses

10.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

11.

Which one of these are not a zero of $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$ ?

a)

0

b)

1

c)

-5

d)

-1

12.

What is the multiplicity of the zero x=1 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

2

b)

1

c)

4

d)

3

13.

What is the multiplicity of the zero x=-5 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

1

b)

2

c)

3

d)

4

14.

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

a)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

b)

$f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

c)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

d)

$f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

15.

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

a)

$f\left(x\right)=x^4\left(x-5\right)^2\left(x-3\right)$

b)

$f\left(x\right)=x^4\left(x+5\right)^2\left(x+3\right)$

c)

$f\left(x\right)=x\left(x-5\right)^4\left(x-3\right)^2$

d)

$f\left(x\right)=x\left(x+5\right)^2\left(x+3\right)^4$

16.

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

17.

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

18.

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)

19.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 with Degree: 7

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

20.

Select ALL the zeros of the equation.

a)

-7

b)

0

c)

-5

d)

-6

21.

Even Multiplicities have which of the following effects on the x-axis?

a)

touches and bounces back

b)

wiggle

c)

crosses the x-axis

22.

Which one of these are not a zero of $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$

a)

-2

b)

0

c)

$-\frac{1}{3}$

d)

-7

23.

How does a multiplicity of 2 affect the graph?

a)

cross

b)

bounce

c)

wiggle (change direction)

24.

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

25.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

26.

What is the multiplicity of an x-intercept?

a)

The highest exponent of a polynomial

b)

The number of different factors

c)

The exponent of the factor corresponding to that x-intercept

d)

The number in front of a polynomial

27.

Given $f\left(x\right)\ =\ \left(2x\ +6\right)^7\left(x-3\right)^4$ ,
what is the multiplicity of the x-intercept $x=-3$ ?

a)

7

b)

2

c)

6

d)

4

28.

Odd Multiplicities have which of the following effects on the x-axis?

a)

Cross the x-axis

b)

Turn on the x-axis

29.

Find the incorrect statement

a)

This function crosses the x-axis at 3

b)

This function is tangent to the x-axis at −4

c)

This function crosses the x-axis at −2

d)

This function crosses the x-axis at 1

30.

State the x-intercepts and whether they will cross or touch the x-axis.

f(x)=3(x–2)(x+5)(x+1)

a)

3 cross, 2 cross, -5 cross, -1 cross

b)

2 cross, -5 cross, -1 cross

c)

3 cross, 2 touch, -5 cross, -1 cross

d)

-2 cross, 5 cross, 1 cross

31.

State the x-intercepts and whether they will cross or touch the x-axis.

y=-4x(x+3)²

a)

4 cross, 0 cross, -3 touch

b)

4 cross, -3 touch

c)

0 cross, -3 touch

d)

4 touch, -3 cross

32.

State the x-intercepts and whether they will cross or touch the x-axis.

f(x)=(x+2)³(x–6)⁴(x²+3)

a)

-2 cross, 6 touch, -3 touch

b)

-2 cross, 6 touch

c)

-2 cross, 6 touch, -3 cross

d)

-2 touch, 6 touch

33.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0 cross , 6 cross , -5 cross

b)

6 cross , -5 cross

c)

0 cross, 6 touch, 5 cross

d)

0 cross , 6 touch , -5 cross

34.

Find the incorrect statement

a)

This function crosses the x-axis at 3

b)

This function is tangent to (touches) the x-axis at −4

c)

This function crosses the x-axis at −2

d)

This function crosses the x-axis at 1

35.

Which function might have the given graph?

a)

f(x) = (x - 6)(x + 4)²

b)

f(x) = (x - 6)²(x + 4)

c)

f(x) = (x + 6)²(x - 4)

d)

f(x) = x(x - 6)(x + 4)

36.

How does a multiplicity of 2 affect the graph?

a)

cross

b)

bounce (touches)

c)

wiggle (change direction)

37.

Is the following written in standard form:
c + 8c³ - 3c⁷

a)

yes

b)

no

38.

Match the following End Behavior to their Graphs

a)

1.

Degree is Odd, Leading Coefficient is Negative

b)

2.

Degree is Odd, Leading Coefficient is Positive

c)

3.

Degree is Even, Leading Coefficient is Negative

d)

4.

Degree is Even, Leading Coefficient is Positive

39.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

40.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

41.

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

42.

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

43.

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

44.

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

45.

Describe the end behavior of the function.
y = 4x¹⁰

a)

down and down

b)

down and up

c)

up and down

d)

up and up

46.

Describe the end behavior of the function. (Put the polynomial in standard form first*)
y = -6x + 4 + 9x³

a)

down and down

b)

down and up

c)

up and down

d)

up and up

47.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

48.

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

49.

Using the above graph what is the sign of the leading coefficient?

a)

Positive

b)

Negative

50.

Determine the end behavior of the graph of

f(x) = 3x⁴ + 2x - 5

a)

As x →∞, f(x) →∞.

As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.

As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.

As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.

As x→-∞, f(x) →-∞.

51.

What is the end behavior of
$f\left(x\right)=4x^5-3x^4+6x-3$ ?

a)

up, up

b)

down, down

c)

up, down

d)

down, up

52.

What is the end behavior of
$f\left(x\right)\ =\ -3x^4+6x^3-7x^2+3x$ ?

a)

up, up

b)

down, down

c)

up, down

d)

down, up

53.

What is the end behavior of
$y\ =\ -4x^7-8x^4+2$ ?

a)

up, up

b)

down, down

c)

up, down

d)

down, up

54.

What is the end behavior of
$y\ =\ 9x^6+x^3+3x^2-3$ ?

a)

up, up

b)

down, down

c)

up, down

d)

down, up

55.

What is the end behavior of
$y\ =\ -5x^3+5x^2+3x-7$ ?

a)

up, up

b)

down, down

c)

up, down

d)

down, up

56.

What is the end behavior of odd degree polynomial functions?

a)

The ends point in opposite directions

b)

The graph is always a parabola

c)

The ends point in the same direction

d)

The graph is always a straight line

57.

What is the end behavior of even degree polynomial functions?

a)

The graph is always a parabola

b)

The ends point in opposite directions

c)

The graph is always a straight line

d)

The ends point in the same direction

58.

The degree of a polynomial can be determined by the largest powered monomial of the polynomial.
What is the degree of the polynomial:
f(x) = 3x² + 4x - 5

a)

Degree 2 (quadratic)

b)

Degree 3 (cubic)

c)

Degree 4 (quartic)

d)

Degree 5 (quintic)

59.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4?

a)

4

b)

7

c)

2

d)

1

60.

Which of the following helps determine end behavior?

a)

The leading coefficient

b)

The number of terms in the function

c)

The y-intercept

d)

The x-intercepts

61.

What is the end behavior as x → -∞ f(x)→ ?

a)

-∞

b)

∞

62.

The two parts of the equation that determine the end behavior are...(select both)

a)

Degree (even/odd)

b)

Leading coefficient (positive/negative)

c)

X-intercepts (positive/negative)

d)

Number of terms (even/odd)

63.

What is the leading coefficient?

a)

Positive

b)

Negative

64.

What is the leading coefficient?

a)

Positive

b)

Negative

65.

What is the degree?

a)

Odd

b)

Even

66.

What is the degree?

a)

Odd

b)

Even

67.

What is the leading coefficient?

a)

Positive

b)

Negative

68.

Given $f\left(x\right)=3x^2-4x^4+2x+1$ .

What is the leading term of the polynomial?

a)

3

b)

$3x^2$

c)

-4

d)

$-4x^4$

69.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

Study Guide- Intro to Polynomials

Total questions: 69

Worksheet time: 2hrs 9mins

Similar Resources on Wayground