Name: ___________________________________________________________________ Period: _____ Table # ____
Unit 4: Polynomials
____
1. Find the sum or difference.

 

 5x 2  2x  1    x 2  5x  2 

 

a.
b.
____
4x 2  3x  3
4x 2  7x  3
5u 5  9u 3  7u  1
11u 5  16u 3  9
c.
d.
11u 5  9u 3  7u  9
5u 5  9u 3  7u  1
c.
d.
x 3  4x 2  8
x 3  14x  8
3. Find the product


x  4   x 2  4x  2 


a.
b.
____
c.
d.
2. Simplify.
 5
 

 3u  9u 3  4    8u 5  7u  5 

 

a.
b.
____
4x 2  7x  1
4x 2  7x  1
x 3  18x  8
x 3  8x 2  14x  8
2
4. Find the missing term: x  3   x 2  6x 
a.
12
b.
3
.
c.
1
6
d.
9
Name: ________________________
____
Table # ____
5. A rectangle has a length of x  9 and a width of x  1. Which equation below describes the perimeter, P,
of the rectangle in terms of x? (Hint, draw a picture and add up all the dimensions)
a.
b.
P = x 2  8x  9
P = 4x  16
c.
d.
6. Find the sum or difference.
 7x 2  3    4x 2  2x  1 

 

7. Simplify.
 5
 

 5s  7s 4  6    8s 5  5s  4 

 

8. Simplify.


3x  2  2x 2  7x  4 


2
P = 2x  8
P=x 8
Name: ________________________
____
Table # ____
2
2
4
9. Which expression is equal to x (3x  2x)  3x ?
a.
b.
2x 2
2x 3
c.
d.
2x 3
3x 3
____ 10. Which factors could represent 36a 10  121b 26 ? (Hint, take the square root of each part, take half of the
exponent)
a.
b.
(4a 2  11b 2 )(9a 5  11b 13 )
(6a 5  11b 13 )(6a 5  11b 13 )
d.
(4a 5  11b 13 )(9a 5  11b 13 )
(6a 5  11b 13 )(6a 5  11b 13 )
c.
d.
17x 2  9x  11
29x 2  15x  11
c.
d.
18x 2  26x  18
18x 2  25x  16
c.
____ 11. Simplify the given expression.

 

 11x 2  3x  19    6x 2  18x  8 

 

a.
b.
17x 2  15x  11
17x 2  21x  27
____ 12. Simplify the given expression.

 

 2x 2  9x  17    16x 2  17x  1 

 

a.
b.
18x 2  8x  18
18x 2  26x  16
3
Name: ________________________
Table # ____
____ 13. Solve the inequality. Graph the solution set.
2(4y – 5)  –10
a.
y0
b.
y
5
8
c.
y0
d.
y
5
8
____ 14. Write in standard form an equation of the line passing through the given point with the given slope.
slope = 5; (1, 2)
a.
–5x + y = 3
b.
5x  y  3
c.
–5x – y = –3
d.
c.
d.
3x 2  6x  40
3x 2  6x  40, R 99
____ 15. Divide 3x 3  3x 2  4x  3 by x + 3.
a.
b.
3x 2  12x  32
3x 2  12x  32, R –93
4
5x + y = –3
Name: ________________________
Table # ____
16. Divide x 2  3x  40 by x  5 .
17. Simplify x  1 x 3  3x 2  x  2
18. ** Simplify x  3 x 4  3x 2  x  4
5
Name: ________________________
Table # ____
____ 19. Divide
 3

 k  8   k  2


a.
b.
k 2  2k  4
k 2  2k  4
c.
d.
k2 4
k2 4
c.
2x 2  6x  13 +
____ 20. Divide
 3

 2x  5x  4   x  3 


a.
b.
70
x3
21
2x 2  x  7 +
x3
2x 2  6x  23 –
d.
6
43
x3
5
2x 2  x  3 –
x3
Name: ________________________
Table # ____
____ 21. Divide
 4

 4x  12x 3  48x  60   x  4 


a.
4x 3  4x 2  16x  16 +
b.
4x 2  4x  16 +
4
x4
4
x4
c.
4x 2  4x  16 + 4
d.
4x 3  4x 2  16x  16 + 4
c.
2x 2  2x  1
____ 22. Divide
 2

 2x  4x 3  4  10x   2x  3


a.
b.
2
2x  3
1
2x 2  2x  1
2x  3
2x 2  2x  2 +
d.
7
1
2x  3
2
2x 2  2x  2 +
2x  3
Name: ________________________
Table # ____
23. Divide
 3

 2x  9x 2  3x  6   x  4 


24. Divide
 3

 2x  6x 2  16x  24   x  5 


____ 25. Solve the equation. Check your solution.
10  2x  4
a.
b.
c.
d.
5
–9
–3
7
8
Name: ________________________
Table # ____
26. Jeff earns $4.00 an hour baby-sitting. He is saving to buy a pair of in-line skates that costs $116.00. If Jeff
already has $60.00 saved, how many hours must he baby-sit in order to buy the skates?
27. Find the perimeter.
28. Evaluate the expression 16 + 12x – x 3 when x = 3.
29. Write an equation of the line that passes through (2, 1) and is parallel to the line y  2x  7 .
9
Name: ________________________
Table # ____
30. Find the domain and range in set-builder notation.


____ 31. A rectangle has an area of  x 3  14x  8  square meters and a width of x  4  meters. Find its length, in


terms of x.
a.
b.
 2

 x  14  meters


 2

 x  4x  2  meters


c.
d.
32. Divide using synthetic division.
 2x 3  7x 2  6x  15   x  4 


10
 2

 x  2  meters


 2

 x  4x  14  meters


Name: ________________________
Table # ____
33. The volume of a rectangular box is 9x 3  18x 2  x  2 and its width is 3x  1. Find the measurement of the
length and height of the box.
____ 34. The volume of a shoebox can be expressed as x 3  13x  12 . The height of the box is x  1. Which of the
following expressions could represent the width and length of the box?
a.
b.
(x + 4)(x + 3)
(x - 4)(x + 3)
c.
d.
11
(x - 3)(x+ 4)
(x - 3)(x - 4)
Name: ________________________
Table # ____
3
2
35. Use synthetic division to find P(3) P(x)  x  x  15x  9.
3
2
3
2
36. If P(x)  x  4x  8x  6 , find P(2) . Then use synthetic division for (x  4x  8x  6)  (x  2).
____ 37. Factor
3x 2  x  14
a.
b.
x  7  3x  2
3x  7 x  2 
c.
d.
12
x  7  3x  2
3x  7 x  2 
Name: ________________________
Table # ____
____ 38. Factor the expression.
9y 2  16
a.
b.
(3y  4)(3y  4)
(9y  1)(y  16)
c.
d.
(3y  4)(3y  4)
(3y  4)(3y  4)
____ 39. Write the expression as a complex number in standard form.
2  4i  3  9i
a.
5  13i
b.
30  30i
c.
1  5i
d.
1  5i
40. Write the expression as a complex number in standard form.
3  7i 1  2i
____ 41. Use the quadratic formula to solve: x 2  3x  1 = 0
a.
b.
3 
2
3
5
5
2
,
,
3 
2
3
5
5
2
c.
d.
13
3
13
2
,
3
13
2
3  13 3  13
,
2
2
Name: ________________________
____ 42. Plot the number in a complex plane 2  4i.
a.
b.
Table # ____
c.
d.
3
2
43. Given that P(3) = 0, factor P(x)  x  7x  15x  9
14
Name: ________________________
Table # ____
3
2
44. Given that P(2)  0 , factor P(x)  2x  7x  7x  2
3
2
45. ** Given that P(0)  0 , factor P(x)  2x  7x  6x
15
Name: ________________________
Table # ____
3
46. **Given that (x  1) is a factor of P(x) , factor P(x)  x  21x  20
____ 47. Solve. Graph your solution. x  3   3
a. x  –6 or x  0
b.
–6  x  0
c.
x  –6 or x  0
d.
–6  x  0
48. Factor x 3  64
16
Name: ________________________
Table # ____
49. Factor x 3  1000
50. Factor 125x 3  27
51. Factor 8x 3  125
52. Factor 3x 3  3
53. Factor 40x 3  5
3
3
54. *Factor the polynomial completely. x  8y
3
3
55. *Factor the polynomial completely. 64x  27y
17
Name: ________________________
Table # ____
56. Given polynomial f(x) and a factor of f(x), factor f(x) completely.
f x   2x 3  3x 2  8x  3 x  3
57. Given polynomial f(x) and a factor of f(x), factor f(x) completely.
f x   x 3  6x 2  11x  6 x  2
58. Solve x 3  27  0
18
Name: ________________________
Table # ____
59. Solve x 3  64  0
3
60. Find the roots for y  x  125
3
61. Find the roots for f(x)  64x  8
19