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Homework MAT220 Algebra and Trigonometry Review
Be sure to work on some of these problems each day during our review time! All of these problems should be done
WITHOUT the use of a calculator!
0. Lines (we talked a little bit about this on Day #1…how much do you remember from your previous math courses?).
1. What “type” of lines have a slope of zero? ____________________________
2. What “type” of lines have a slope that is undefined? _________________________
3. Find the equation of the line that passes through the two points  2, 5
and
3,7  .
Write your final answer in
slope-intercept form.
I. Completely Factor the following.
1. 6n2  27n  168
2. 2 x3  6 x2  8x  24
3. y 2  6 y  9
4. 3a5  24a 2
5. n3  216
6. 6 x2  7 x  3
7. m2  9n2
8. 18a 2b  15ab2
9. x3  2 x2  9 x  18
10. 3m4  48
11. 8x2  19 x  15
12. 8x2  2 x  15
13. 8x2  37 x  15
14. 8x2  14 x  15
15. 12 x2  14 x  6
16. x6  2 x5  x4  x2  2 x  1 (Hint: try “grouping” 3&3)
17. 4c2  4cd  d 2
18. m6  8m3  20
19. p  64 p 4
20. 125a  8a 4
( GCF) Factor out the GCF
(and simplify if possible, fractions and negative symbols should be out front)
1. x2e x  2 xe x
2.
2
3
2
 x  1  2 x   4  x  1  x2 
3
II. (adding zero) Complete the square to transform the quadratic function into the “graphing form”
f  x  a  x  h  k
2
2
1. f  x   2 x  4 x  6
III. Working with Fractions
(Properties of Fractions) True or False?
x 1
x  3 x2  3 x  1 x  1
1.
____________________________



x6
3
x  6 1 2
1 2
35 3 5
  ________________________
2.
6
6 6
45 4 5
  __________________________
3.
7
7 7
2
4.
5.
6.
7.
8.
9.
x 2  5 x  6  x  6  x  1  x  6   x  1 x  6



x2 1
 x  1 x  1  x  1  x  1 x  1
x  1 ______________________
x y x y
 
_________________
2 3
5
x y x y
 
___________________
2 3
6
a
a 1 1 a
    ____________________
bc b c b c
a
a a
  ________________________
bc b c
x
x x
__________________________
 
25 2 5
(Multiplying by 1) Perform the indicated operation, simplify if possible.
1.
3 1

4 6
2.
9x  2
7
 2
3x  2 x  8 3x  x  4
3.
x 2  x  12 x 2  2 x  24
 2
x2  6x  8
x  x6
2
(conjugation) Rationalize the denominator by “multiplying by 1”. Be sure to simplify your result and give a complete
answer.
1.
x7
3 x  2
2.
x 1
2 3 x
(Simplifying Algebraic Fractions) Simplify the following fractions
(be sure to write x 
if applicable)
1.
x2  x  6
x2  4
2.
x 2  2 x  15
x3  3x 2  9 x  27
x2 1
3. 3
x  3x 2  3x  1
IV. (Finding zeros of Polynomial Functions)
Find all of the zeros for each of the following polynomial functions.
1. f  x   2 x5  x 4  2 x  1
2. f  x   6 x 4  11x3  13x 2  16 x  12
3. f  x   x5  2 x 4  4 x3  8x 2  3x  6
V. Graphs of Relations
(Absolute Value functions)
1. Write f  x   3x  6 as a piecewise defined function (using the definition of absolute value). Be sure to show
exactly where the domain is split.
(Piecewise defined functions)
 x 2  7

1. Graph g  x    6  x
x  5

x 1
1 x  7
x7
2. Write a piecewise defined function for the graph given below…
VI. Trigonometry
Find each of the following… Draw a partial unit circle for #1,2,3 and 5 to show where you obtained your answers. For #4
draw an appropriate triangle.
 3 
1. tan  
 4 
 
2. cos  
2
 1
3. sin 1   
 2

 3 
4. sin  cos 1   
 5 

  5  
5. tan 1  tan   
  6 
(Simplifying Trigonometric Fractions) Simplify the following fractions
(be sure to write x 
if applicable)
1.
cos 4 x  sin 4 x
2cos 2 x
2.
sin 2 x
sin x
3.
1  sin x
cos 2 x
If you need extra practice on any of these topics just go to the Homework page on my Precalculus web page and find the relevant
section! You can find solutions to all of the Precalculus homework problems on the Precalculus HELP page. Note: You will NOT find
practice with the x  part of the last three problems as we do not typically cover solving trigonometric equations before we cover
simplifying trigonometric fractions. See the section on solving trigonometric equations if you need a refresher on that.
One last problem to consider as we finish this review and move on to Calculus.
When will the function f  x  
 x  c
m
 x  c
n
have a “hole” at x = c and when will it have a “vertical asymptote” at x = c ?
What is the relationship between n and
m that determines this?