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Algebra 2 upTo Solving Polynomial

Total questions: 50

Worksheet time: 2hrs 23mins

Name
Class
Date
1.
If given the equation
y = 3(x + 5)2 - 4,
what is the vertex of the parabola?
a)
(5, -4)
b)
(-5, -4)
c)
(-15, -4)
d)
(15, -4)
2.
Which of the following is a solution to the function?  (x - 8)(x - 9) = 0
a)
8
b)
-9
c)
-17
d)
0
3.
Give the x-intercept
3x + 8y = 24
a)
(8, 0)
b)
(0, 8)
c)
(3, 0)
d)
(0, 3)
4.

Subtract the two complex numbers and put your answer in a + bi form.

(10+3i) - (2-9i)

a)

20-27i

b)

12-7i

c)

8+12i

d)

20-27i2

5.

(1-3i)(2+5i)

** Remember i * i = i 2 and i 2 = -1

a)

22-i

b)

16-i

c)

17-i

6.

Factor completely:

3x2 + 18x +15

a)

3(x2 + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

7.
Simplify the expression.
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3 
b)
-7n2 - 8n + 3 
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
8.
What is the End behavior on the left side
a)
x →-∞, y→∞
b)
x →∞, y→-∞
c)
x →-∞, y→-∞
d)
x →∞, y→∞
9.
What piece of information does c identify in the following equation?
y=ax2+bx+c
a)
Zeroes
b)
Axis of Symmetry
c)
Direction
d)
y-intercept
10.
What form is the equation in?
y = 2x2-8x+7
a)
Standard
b)
Vertex
c)
Factored
d)
None of These
11.
What is the degree of the polynomial function
P(x)=3x4-7x2-2x7-x+4?
a)
4
b)
7
c)
2
d)
1
12.

What is the leading coefficient of the function:

f(x) = 6x2 + 4 - 3x4 + 5x - 9x3

a)

6

b)

3

c)

-3

d)

4

13.

A function with degree 3 is called

a)

constant

b)

cubic

c)

linear

d)

quadratic

14.
Choose the answer that represents the rationalized complex number.
a)
(4-3i)/25
b)
35/(16-9i)
c)
20i/(4-3i)
d)
(3+4i)/5
15.
Choose the answer that represents the rationalized complex number.
a)
(20+30i)/-5
b)
-4-6i
c)
(20+30i)/13
d)
(20-30i)/13
16.

Convert from standard form to vertex form: m2 + 10m + 16 = 0

a)

(m - 5)2 - 9

b)

(m + 5)2 - 9

c)

(m - 5)2 + 9

d)

(m + 5)2 + 9

17.
Solve the equation by completing the square and then finding the roots. 
x2+ 6x - 4 = 36
a)
x = -7, 7
b)
x = 4, -10
c)
x = -4 +- √7
d)
x = 10, -4
18.

Use the functions

f(x)=3x−11, g(x)=x2+6x, and h(x)=x+2.

Write the function rule.

(f+g)(x)=

a)

x2 + 9x + 11

b)

x2 + 9x - 11

c)

3x2 + 7x - 66

d)

none of the above

19.

Does this graph have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

20.
Does
y = -4x2
have a maximum or minimum value?

a)
maximum
b)
minimum
21.
In slope intercept form (y=mx+b) what is the "m"?
a)
The y-intercept
b)
The x-intercept
c)
The slope (rate of change)
d)
A point
22.
In slope intercept form (y=mx+b) what is the "b"?
a)
The y-intercept
b)
The x-intercept
c)
The slope (rate of change)
d)
A point
23.
Which equation represents the following graph?
a)
y = 3x + 2
b)
y = -2x + 3
c)
y = 2x + 3
d)
y = -3x + 2
24.

Simplify

a)

y2z10√xy

b)

20yz√xy

c)

xy2z10√y

d)

yz6√xy2z2

25.
Find the equation of the line that passes through the points:
(-4, -2) and (-3, 5)
a)
y = 1/7 x + 26
b)
y = 7x + 26
c)
y = -7x + 26
d)
y = -7x - 26
26.
Factor:
x2 + 5x - 24
a)
(x - 8)(x + 3)
b)
(x + 8)(x - 3)
c)
(x + 6)(x - 4)
d)
(x + 12)(x - 2)
27.
|−4 + 5x| = 16
a)
{16/5,12/5}
b)
{4,-5}
c)
{-12/5, 4}
d)
4
28.
Is this mapping a function or not a function? 
a)
Function
b)
Not a Function
29.
Given 
f(x)= 2x2 + 5x - 17, find f(-1). 
a)
f(-1) = -20
b)
f(-1) = -24
30.
Given f(x) = -4x - 10 and f(x) = 10. Find x
a)
x = -5
b)
x = 5
c)
x = -50
d)
x = 30
31.
For synthetic division, what would be the number in the left hand box?
a)
0
b)
1
c)
2
d)
3
32.
(2x3 - 5x - 7) ÷ (x - 2)
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
33.

Is this division problem worked out correctly?

a)

This is correct!

b)

This is incorrect!

34.
What is the proper way to write the answer for the following problem? 
a)
2x3-x2-25x-12
b)
2x4-x3-25x2-12x+0
35.
What is the remainder of  (3x3 -5x2 -4x +1) ÷ (x + 3)?
a)
-25
b)
25
c)
113
d)
-113
36.
The polynomial is...
a)
Odd degree, positive leading coefficient.
b)
Odd degree, negative leading coefficient.
c)
Even degree, positive leading coefficient.
d)
Even degree, negative leading coefficient.
37.
Determine the values of
a, b, and c for
the quadratic equation: 
4x2 – 8x = 3
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
38.
x2 - 169
a)
( x - 13) ( x + 13) 
b)
( x + 13) ( x + 13) 
c)
( x - 13) ( x -13) 
d)
Prime
39.

Completely factor the Following

4x2-16

a)

(2x-4)(2x+4)

b)

(4x-4)(4x+4)

c)

4(x-2)2

d)

4(x-2)(x+2)

40.
Solve
x2 + 8 = 6x
a)
2, 4
b)
-2, -4
c)
-2, 4
d)
2, -4
41.
Solve
 2x² - 3x - 2 = 0
a)
x = 1, x = -1
b)
x = -1/2, x = 2
c)
x = 1/2, x = 2
d)
x = 1/2, x = 1
42.

4x + 3y = 2x +18 and 2y + 3 = 3x - 13


The above lines are:

a)

Perpendicular

b)

Parallel

c)

Neither parallel nor perpendicular

d)

the same line

43.

Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost of one small box of oranges.

a)

$7

b)

$13

c)

$20

d)

$6

44.
Solve by elimination:
3x+7y=23

-3x-7y=-17
a)
No solution
b)
ARN
c)
(-3,3)
d)
(3,3)
45.
Solve by elimination
-12x-4y= -8 
  -6x-2y= -4
a)
no solution 
b)
(0,0)
c)
infinitely many solutions 
d)
(4,0)
46.

Gym A has a monthly fee of $50 and no registration fee. Gym B has a monthly fee of $10 and a $160 registration fee. After how many months will Gym A have a better value than Gym B?

a)

2

b)

3

c)

5

d)

4

47.

Solve the following system of equations:

y + 4x=8

5x + 2y=13

a)

x = 1

y = 4

b)

x = 2

y = 2

c)

x = 4

y = 1

d)

NONE OF THE ABOVE!!!!

48.
Write the equation in vertex form:
y = -2x2+16x+4
a)
y=-2(x-4)2+4
b)
y =-2(x+4)2+36
c)
y=-2(x+4)2+4
d)
y =-2(x-4)2+36
49.

(X3+3x3+1)(3x2+6x-2)

a)

3x5+9x5+6x4+18x4-2x3-6x3+3x2+6x-2

b)

12x5+24x4-8x3+3x2+6x-2

c)

12x10+24x4-8x6+3x2+6x-2

d)

12x5+24x4+8x3+3x2+6x-2

50.

Find the volume of a tank whose base has an area of 3x2+30x+5 square feet and whose height is 8x-5 feet.

a)

24x3+225x2-110x-25

b)

24x3+240x2-15x2+40x-150x-25

c)

24x3+225x2+110x-25x

d)

24x3-225x2+110x-25x

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