Free Printable Test 4 REVIEW

1.

Which of the following functions are NOT polynomial functions?

a)

$f(x)=x^2+2$

b)

$f(x)=3x-2x+\sqrt{x}$

c)

$f(x)=3x^2-\frac{2}{x}$

d)

$f(x)=12-x^4+3x^{-2}$

e)

$f(x)=3x^{11}-2x^{13}$

2.

Which expression simplifies to a quadratic binomial?

a)

$(3x^2-5a-1)+(2a+7a-1)$

b)

$(2x-5)(2x+5)$

c)

$(x^2+1)^2$

d)

$\frac{6x^6-3x}{3x^2}$

3.

Which of the following descriptions is not true about the polynomial?

a)

Fifth Degree polynomial

b)

Sixth Degree Polynomial

c)

... has negative coefficient

d)

Odd Degree polynomial

4.

By inspection, which of the following best describes the graph of the polynomial function $y=x^3-4x^2+3x-12$ ?

a)

Graph falls to the left and rises to the right.

b)

Graph rises to the left and falls to the right.

c)

Graph rises on both sides.

d)

Graph falls on both sides.

5.

How do you describe the behavior of the graph if the degree is even and the leading coefficient is negative?

a)

The graph rises to the left and falls to the right.

b)

The graph falls to the left and rises to the right.

c)

The graph falls on both sides.

d)

The graph rises on both sides.

6.

By inspection, where is the turning point of the graph of $f(x)=x^4+1$ located on the cartesian plane?

Hint: solve for x-intercepts and observe end behavior

a)

above the x-axis

b)

below the x-axis

c)

on the x-axis

d)

on the y-axis

7.

Determine the remainder of $(9x^2-6x+2)$ divided by $x-3$ .

8.

If ( p(x) ) is divided by ( (2x - 1) ) using synthetic division, the value indicator to be used will be equal to ________.

9.

If ( p(a) ) is divided by (a+1) , and the remainder is equal to zero, then (a+1) is a (a) of p(a).

10.

What is the degree of $f(x)=(x+3)(x-4)^2(x+1)^5?$

11.

Which factor in $f(x)=(x+3)(x-4)^2(x+1)^5$ has a multiplicity of 5?

a)

(x + 3)

b)

(x - 4)

c)

(x + 1)

12.

Which of the following is a true statement about the graph of $\left(p(x)=(x-4)(x+2)(3x^2+6x\right)?$

a)

The graph crosses the x-axis four times and is never tangent to the x-axis.

b)

The graph crosses the x-axis three times and is never tangent to the x-axis.

c)

The graph crosses the x-axis twice and is tangent to the x-axis once.

d)

The graph crosses the x-axis three times and is tangent to the x-axis once.

13.

Write the polynomial function with the least degree in factored form (whose a =1) that is represented by the given graph.

14.

What are the x-intercepts of the graph of $y=(x-3)(x+1)(x-1)?$

x = { (a) }

15.

A fifth degree polynomial function is shown below. Which of the statements are NOT true about this function?

a)

Leading coefficient is positive

b)

Only two relative maximums

c)

Only two intervals of increasing

d)

Positive from

x = -2 to x = 1.75

e)

Exactly 5 zeros

16.

Which zero will "bounce" off of the x-axis for x(x - 1)²(x + 2)(x + 3)

a)

-1

b)

1

c)

-2

d)

-3

17.

What degree is the graphed polynomial?

a)

Even positive a value

b)

Odd positive a value

c)

Even negative a value

d)

Odd negative a value

18.

For the pictured polynomial, how many relative minimas are there?

a)

1

b)

2

c)

3

d)

4

19.

For the pictured polynomial, at which interval is it increasing?

a)

(0, 2)

b)

(2, 3.5)

c)

(3.5, ∞)

d)

(2,4)

20.

For the pictured polynomial, at which interval is it decreasing?

a)

(-∞, 2)

b)

(-2, 0)

c)

(0, ∞)

d)

(-3, 1)

21.

For the pictured polynomial, which is a relative max?

a)

(-3, -2)

b)

(3, 0)

c)

(2, 0)

d)

(4, 1)

22.

For the pictured polynomial, determine in (x,y) the absolute maximum point.

(a)

23.

Which root has a multiplicity of 2?
(provide the value only)

24.

On the interval of (0, 2) what is happening?

a)

the graph is decreasing

b)

the graph is increasing

c)

the graph remains constant

25.

Complete the table for Q2:

26.

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

a)

$As\ \ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$ $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty$

b)

$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$ $As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$

As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty

d)

$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$

As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty

27.

What is the end behavior of this function: $f\left(x\right)=-2x^6+7x^2-8$

a)

$As\ \ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty\$

As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty

b)

$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty

c)

$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$

As\ x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty

d)

$As\ \ x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$

As\ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow+\infty

28.

Abigail is tracking the height of a ball thrown into the air. The graph shows the ball's height over time. Identify the y-intercept of the graph.

a)

(0, -3)

b)

(0, 1)

c)

(0, 3)

d)

(2, 1)

29.

Find the decreasing interval

a)

(-1, infinity)

b)

(-infinity, -1)

c)

(-infinity, 4)

d)

(4, infinity)

30.

Write this polynomial in standard form:

$100a+45a^2-14a^3-54a^7$

31.

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

a)

x + 1

b)

x + 2

c)

x + 5

d)

x + 10

32.

What are the three factors for
(x³ +7x² +7x -15) ÷ (x -1)?

a)

(x-1) (x+5) (x-3)

b)

(x-1) (x+5) (x + 3)

c)

(x+1) (x+5) (x-3)

d)

(x+1) (x-5) (x-3)

33.

Match the following appropriately.

It is important you can recognize the connection between factors and solutions.

a)

x + 3 is a factor of p(x).

1.

-3 is a solution of p(x).

b)

x - 5 is a factor of p(x).

2.

5 is a solution of p(x).

c)

3x - 5 is a factor of p(x).

3.

5/3 is a solution of p(x).

d)

x + 5 is a factor of p(x).

4.

-5 is a solution of p(x).

34.

If $\left(x-4\right)$ is NOT a factor of f(x), then...

a)

$f\left(4\right)=0$

b)

$f\left(-4\right)=0$

c)

$f\left(4\right)\ne0$

d)

$f\left(-4\right)\ne0$

35.

Which of the following shows the correct set up to prove that an x-intercept is a solution?

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

a)

$\left(-3\right)^2+2\left(-3\right)-3\ and\ \left(1\right)^2+2\left(1\right)-3$

b)

$\left(3\right)^2+2\left(3\right)-3\ and\ \left(-1\right)^2+2\left(-1\right)-3$

c)

$\left(-3\right)^2+2\left(-3\right)-3\ and\ \left(-1\right)^2+2\left(-1\right)-3$

d)

$\left(3\right)^2+2\left(3\right)-3\ and\ \left(1\right)^2+2\left(1\right)-3$

36.

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

37.

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

38.

Divide: $\frac{6x^2+7x-20}{2x+5}$

a)

$6x^2-8x$

b)

$6x-8$

c)

$3x-4$

d)

$3x^2-4x$

39.

Divide: $\frac{2x^4-9x^3+21x^2-26x+12}{2x-3}$

a)

$x^3-3x^2+6x-4$

b)

$2x^3-6x^2+12x-8$

c)

$x^4-3x^3+6x^2-4x$

d)

$2x^4-6x^3+12x^2-8x^{ }$

40.

Divide: $\frac{3x^3-4x^2-9x+10}{x-2}$

a)

$3x^2+2x-5$

b)

$3x^3+2x^2-5x$

c)

$3x^2-10x^{ }-29-\frac{48}{x-2}$

d)

$3x^2-10x-29+\frac{48}{x-2}$

41.

Is $(x-2)$ a factor of $f(x)=x^3-8x^2+14x-4$ ?

a)

Yes, (x-2) is a factor.

There is a remainder.

b)

No, (x-2) is not a factor.

The remainder is zero.

c)

Yes, (x-2) is a factor.

The remainder is zero.

d)

No, (x-2) is not a factor.

There is a remainder.

42.

What should be the correct order of the coefficients when setting up synthetic division for $(3x-4x3+6x4+1)\div(x+3)$ ?

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

43.

If you were dividing $x^6+4x^3+2$ , how many 0's would you need as placeholders when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

44.

Which graphs have a POSITIVE leading coefficient? (Check all that apply)

a)

b)

c)

d)

e)

45.

$\$ Which graph depicts the function $f\left(x\right)=\left(x-2\right)^2\left(x-8\right)?$

a)

b)

c)

46.

Which is the equation for the graph shown?

a)

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

b)

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

c)

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

d)

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

47.

Express the END BEHAVIOR of the function: $f\left(x\right)=-12x^7-19x^3+22$

a)

x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\

x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty

b)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

d)

$x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty$
$x\rightarrow-\infty,\ f\left(x\right)\rightarrow\infty$

48.

Classify this polynomial by degree and classification.

6x^3

a)

Cubic

b)

Linear

c)

Monomial

d)

Trinomial

49.

Which of the following is NOT a polynomial?

a)

$7x^2+1$

b)

$\frac{7x}{3}$

c)

$\frac{7}{x+3}$

d)

$10x^2+5x-1$

50.

Which of the following are NOT polynomials? There's more than 1!

a)

$20x^3+5x^{-2}$

b)

$\frac{5}{8x}$

c)

$\frac{7x+1}{20}$

d)

$x$

51.

$2\sqrt{3x}+x^2-1$

a)

Polynomial

b)

Not a Polynomial

52.

What is the degree of the polynomial?

m\left(x\right)=x\left(x+5\right)\left(x-6\right)

a)

3

b)

2

c)

9

d)

6

53.

What are the zeros with multiplicities?

g(x)=(x+4)^2(x+8)^3(x-5)

a)

-4 multiplicity 1, -8 multiplicity 1, 5 multiplicity 3

b)

4 multiplicity 2, 8 multiplicity 3, -5 multiplicity 1

c)

4 multiplicity 3, 8 multiplicity 2, -5 multiplicity 1

d)

-4 multiplicity 2, -8 multiplicity 3, 5 multiplicity 1

54.

What are the zeros with multiplicities?

h(x)=(x-2)(x-5)(x+6)

a)

2 multiplicity 1, 5 multiplicity 1, 6 multiplicity 1

b)

-2 multiplicity 1, -5 multiplicity 1, -6 multiplicity 1

c)

2 multiplicity 1, 5 multiplicity 1, -6 multiplicity 1

d)

-2 multiplicity 1, -5 multiplicity 1, 6 multiplicity 1

55.

What is the equation of a polynomial with 5 factors of (x – 5), 6 factors of (x + 5), and 4 factors of (x + 4)?

a)

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

b)

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

c)

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

d)

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

56.

Find the incorrect statement

a)

This function passes through the x-axis at 3

b)

This function touches and turns around at −4

c)

This function passes through the x-axis at −2

d)

This function passes through the x-axis at 1

57.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

58.

Find a polynomial function of degree 3 with zeros 3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

59.

Over the interval (−1, 2), the graph of the polynomial shown could be described as

a)

decreasing

b)

increasing

c)

quadratic

d)

complex

60.

Given $f(x)=x^3−6x+k$ , and $x-2$ is a factor of $f\left(x\right)$ , then what is the value of $k$ ?

61.

Given $f(x)=x^3+kx+1,$ , and $x-1$ is a factor of $f\left(x\right)$ , then what is the value of $k$ ?

62.

Given $f(x)=2x^3+x+k$ , and the remainder when f(x) is divided by $x+1$ is -4, then what is the value of $k$ ?

63.

Given $f(x)=2x^2+kx−1$ , and the remainder when f(x) is divided by $x-2$ is 11, then what is the value of $k$ ?

64.

Which of the following is a polynomial function?

a)

$f(x) = \frac{1}{x^2 + 1}$

b)

$f(x) = x^3 - 4x + 7$

c)

$f(x) = 2^x$

d)

$f(x) = \sqrt{x + 3}$

65.

What is the degree of the polynomial? $f\left(x\right)=-2x\left(x+3\right)^2\left(x-7\right)\left(x+5\right)^3$

66.

A polynomial's end behavior is determined by the (a) and the (b) of the leading term.

Choose from the below words

factors

zeros

roots

degree

sign of the leading coefficient

67.

When constructing a polynomial from its graph, you must consider the (a) , the (b) of each root, and the (c) of the graph.

Choose from the below words

x-intercepts

multiplicity

end behavior

degree

leading coefficient

standard form

68.

Which is true about the equation of the graph shown?

a)

The function has an Odd degree

b)

The function has an Even degree

c)

The function has 5 real zeros

d)

The function has a positive leading coefficient

69.

Select the two descriptions that best describe the polynomial FUNction's graph.

a)

Even degree

b)

Odd degree

c)

Positive leading coefficient

d)

Negative leading coefficient

70.

How is this rational function transformed from the parent function: $y=\frac{3}{x}$

a)

Stretched by a factor of 3

b)

Compressed by a factor of 3

c)

Shifted up by 3

d)

Shifted down by 3

71.

Select all transformations which are true for the equation: $f\left(x\right)=\frac{a}{\left(x-h\right)}+k$

a)

Stretches by a factor of a (if a > 1)

b)

Translates right by h

c)

Translates up by k

d)

Compresses by a factor of a (if 0 < a < 1)

e)

Reflects vertically if 'a' is negative (a < 0)

72.

Which of the following is used to find the y-intercepts of a rational function?

a)

Set the numerator equal to 0

b)

Set the denominator equal to 0

c)

Plug 0 into the simplified function

d)

Compare the degrees of the numerator and denominator.

73.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,\ 0\right)U\left(0,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)U\left(-2,\ \infty\right)$

d)

$\left(-\infty,\infty\right)U\left(\infty,\ \infty\right)$

74.

Describe the transformations from the parent function.

a)

Left 3, up 1

b)

Left 1, up 3

c)

Right 3, down 1

d)

Right 1, down 3

75.

Simplify.

a)

$\frac{\left(m+6\right)}{\left(m-3\right)}$

b)

$\frac{7}{\left(m-3\right)}$

c)

$7\left(m+6\right)$

d)

$\left(m-3\right)$

76.

How else can you write $\sqrt{x}$ ?

a)

$x^{\frac{1}{2}}$

b)

$x^2$

c)

$x^{-2}$

d)

$x^{\frac{1}{4}}$

77.

$8^{\frac{1}{3}}$

a)

-2

b)

4

c)

$\frac{8}{3}$

d)

2

78.

Rewrite as a radical expression

$4^{\frac{2}{7}}$

a)

$\sqrt[]{4^7}$

b)

$\sqrt[7]{4^2}$

c)

$\sqrt[4]{2^7}$

d)

$\sqrt[]{7^4}$

79.

Use the Properties of Exponents to simplify

$\left(a^2\right)^{\frac{4}{9}}$

a)

$a^{\frac{6}{9}}$

b)

$a^{\frac{22}{9}}$

c)

$a^{\frac{8}{9}}$

d)

$a^{\frac{11}{9}}$

80.

Rewrite x^3/4 in radical form

a)

³√(x)⁴

b)

⁴√(x)³

c)

^x√(3)⁴

d)

1/(³√(x)⁴)

Test 4 REVIEW

Total questions: 80

Worksheet time: 4hrs 7mins

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