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Pre-calc unit 3 polynomial and power functions

Total questions: 50

Worksheet time: 3hrs 30mins

Name
Class
Date
1.

what is the degree of the function f(x)=x3-4x2+2x+3?

a)

3

b)

2

c)

4

d)

1

2.

how many turning points does the function f(x)= 3x3+5x2-x-2 have?

a)

1

b)

3

c)

0

d)

2

3.

what is the sum of the roots of the function f(x)=x3-4x2+x+3?

a)

4

b)

3

c)

2

d)

6

4.

The correlation coefficient is a number "r" such that:

a)

-1<r<1

b)

-1>r>1

c)

-1≤r≤1

d)

-1≥r≤1

5.
The table shows the average braking distances of a car at various speeds.  The braking distance is the distance the car travels before coming to a stop after its breaks are applied.  Use a quadratic model to predict the breaking distance at 70mph.  
a)
245 ft
b)
225 ft
c)
285 ft
d)
265 ft
6.

What is the degree of the following polynomial?

f(x)= 5x5+3x3-2

a)

4

b)

3

c)

1

d)

5

7.
What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x3 - 5x2 + 2x - 10
a)
0
b)
2x-10
c)
-2x-10
d)
2x+10
8.

Is (x-4) a factor of (x3 +x2 -16x-16)?

a)

YES

b)

NO

c)

I don't know

9.
What is the proper way to write the answer for the following problem? 
a)
2x3-x2-25x-12
b)
2x4-x3-25x2-12x+0
10.
Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x3 + 2x2 - 6x + 8
a)
±1, ±8
b)
±1, ±2, ±4, ±8
c)
±1, ±2, ±4
d)
1, 2, 4, 8
11.

Which of the following graphs has an odd degree with a positive leading coefficient?

a)
b)
12.
2x2 - 6x - 7 = 0
What are the sum and the product of roots?
a)
Sum = 3
Product = 7/2
b)
Sum = - 3
Product = - 7/2
c)
Sum = - 3
Product = 7/2
d)
Sum = 3
Product = - 7/2
13.
Which function has this end behavior?
a)
-x2-3x+1
b)
-x3+2x2+3
c)
x4+3x3-4x+1
d)
x5-4x4+2x2-1
14.

The degree of a polynomial determines...

a)

the maximum number of x-intercepts

b)

the number of turning points

c)

if the end behavior is up or down

d)

the y-intercept

15.
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)
16.
When a polynomial function f(x) is divided by
 (x - 8), the remainder is 12. 
What is f(8)?
a)
-8
b)
8
c)
12
d)
cannot be determined
17.

(x2+4x-45)⁄(x+9) (use synthetic division)

a)

x+5

b)

-x+5

c)

-x-5

d)

x-5

18.

How many possible negative real roots does the following polynomial have?

f(x) = x4 - 3x3 - 17x2 + 39x -20

a)

3 or 1

b)

3

c)

1

d)

2 or 0

19.

how many possible positive real roots does the following function have? f(x)=x4-x3+6x2+3x-2

a)

1

b)

2

c)

3

d)

4

20.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.

(4, -7); m = -1/4

a)

y= -1/4(x - 4)-7

b)

y= -1/4(x + 7)+4

c)

y= 4(x - 4)-7

d)

y= -1/4(x - 4)+7

21.

when the function f(x)=6x3+11x2-x-6 is synthetically divided by 2, all the values in the depressed line are positive. Is 2 an upper bound?

a)

yes

b)

no

c)

I don't know

22.

when the function f(x)=2x3-x2-7x-3 is synthetically divided by -3, all the values in the depressed line have alternating signs. Is -3 an upper bound?

a)

yes

b)

no

23.

find the roots of the following equation: x3-6x2+11x-6=0

a)

x=1,2,3

b)

x=-2, 1, 5

c)

x=1/2, 3, 4

d)

x=-1,4

24.

The function f(x)=x3-4x2+2x+3 can be written as...

a)

(x-4)(x2-2x-3)

b)

(x2-1)(x-3)

c)

(2x-1)(x-4)

d)

(x-3)(x2-x-1)

25.
Johnny has to pay $15 for a large pizza and 1.50 for each topping.  What is the meaning of the y-intercept?
a)
It cost 1.50 per topping
b)
It cost 1.50 for unlimited toppings
c)
It cost $15 for a large pizza
d)
It cost $15 for a large pizza with no toppings
26.

The height of a water balloon that is launched into the air is given by h(t) = -5x2+20x+25. When will the balloon explode on the ground?

a)

5 seconds

b)

1 second

c)

2 seconds

d)

3 seconds

27.

The height of a water balloon that is launched into the air is given by h(t) = -5t2 + 40t + 2. From what height was the balloon released?

a)

2 meters

b)

5 meters

c)

40 meters

d)

20 meters

28.

(2x3 - 5x2 + 3x + 7) ÷ (x - 2)

a)

2x3 - x2 + x + 9

b)

2x2 - x + 1

c)

2x2 - x + 1 + (9/(x-2))

d)

2x2 - 9x - 15 - (23/(x-2))

29.

(3x3 + 5x - 1) ÷ (x + 1)

a)

3x3 - 3x2 + 8x - 9

b)

3x2 - 3x + 8 - (9/(x+1))

c)

3x2 + 3x + 8 + (7/(x+1))

d)

3x3 + 3x2 + 8x + 7

30.
            Is (x-2) a factor of             f(x)= x3-8x2+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. 
31.
List all the possible rational zeros 
h(x) = x3 - 5x2+2x+12
a)
1,2,3,4,6,12
b)
1,2,6,12
c)
1,2,3,4,6,12,-1,-2,-3,-4,-6,-12
32.
The degree of the polynomial determines the number of roots.
a)
True
b)
False
33.
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
34.
How many zeros does the following function have?
f(x)= x5 - 3x3 + x
a)
8
b)
9
c)
5
d)
3
35.

Which of these is a possible rational root of the polynomials?

x3 - 6x2 - x + 30

a)

0

b)

4

c)

-9

d)

-15

36.
What does multiplicity of a zero mean?
a)
Look at the number of terms
b)
How many times the zero repeats
c)
Find the sum of all the coefficients
d)
Ratio your x and y
37.

A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.

a)

The additional fee of $8.

b)

The initial fee of $25.

c)

The additional fee of $25.

d)

The initial fee of $8.

38.
What is the degree of the polynomial function
P(x)=3x4-7x2-2x7-x+4?
a)
4
b)
7
c)
2
d)
1
39.
Find all zeros of the polynomial function P(x) = x3+6x2+9x+54
a)
6, 3, -3
b)
-6, 3, -3
c)
-6, 3i, -3i
d)
6, 3i, -3i
40.
a)
The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞
b)
The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞
c)
The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0
d)
The end behavior of the graph is x →∞,y→∞and x→⁻∞, y→⁻∞
41.
Is (x-8) a factor of 
(x3-15x2+51x+30)
a)
No
b)
Yes
42.
Is (x-2) a factor of 
(x3+2x2-4x-8)
a)
No
b)
Yes
43.

Identify the missing term to complete the solution.

a)

28

b)

38

c)

48

d)

58

44.

is -1 a lower bound of zeros for the function f(x)=x3-4x2+7 ?

a)

yes

b)

no

c)

not sure

45.

is 2 an upper bound of zeros of function f(x)=x5-4x3+5x+2 ?

a)

yes

b)

no

c)

not sure

46.

Synthetically Divide:

(X4+5X3+6X2-X-2) / (X+2)

a)

X3+3X2-2

b)

X3+2X2-2

c)

5X3+3X2-1

d)

X3+3X2-1

47.
a)
y =  _(x + 2)(x - 1)2
b)
y = -(x - 2)(x + 1)2
c)
y = (x - 2)(x + 1)2
d)
y = -x3
48.

Which equation best represents this graph?

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)2 (x+2)

c)

y = x(x + 3)2 (x - 2)

d)

y = -x(x + 3)2 (x - 2)

49.
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
50.
Describe the end behavior of the graph.
a)
x → ∞, y→ ∞ and x→∞, y→⁻∞
b)
x → ∞, y→ ∞ and x→⁻∞, y→∞
c)
x → ∞, y→ ∞ and x→⁻∞, y→ 0
d)
x → ∞,y→ ∞and x→ ⁻∞, y→ ⁻∞

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