Download 0310 Final Exam Review Factor each polynomial completely: 1. 27x

0310 Final Exam Review
Factor each polynomial completely:
7. Simplify the Complex Fraction:
y
+x
x
x
+y
y
1. 27x3 − y3
2. 5 x3 + 3x 2 y − 2 xy 2
3. x3 + 4 x 2 − 9 x − 36
4. 6 x 2 y 2 + 2 xy 2 − 28 y 2
Divide. Simplify your answer.
8. Solve:
x 2 − 4 x − 12 18 − 3x
÷ 2
x2 − x − 6
x −9
5.
5
4
10
−
= 2
x −3 x+ 2 x − x −6
9. Set up an equation and solve: Working alone
Blitzen can eat a bale of hay in 3 hours, while
Donner can eat it in 6 hours. Eating together, how
long will it take them to eat the bale of hay?
6. Add. Simplify your answer.
2x
x
+ 2
2
x + x − 12 x − 2 x − 3
Simplify each expression. Use only positive exponents. Rationalize all denominators. Assume all variables are
positive. Write complex numbers in the form of a + bi .
10.
11.
12.
3
16x9 y 3
14.
50x7 y 9
⎛ 25 ⎞
15. ⎜ ⎟
⎝ 16 ⎠
2
7
13. 10 12 x3 + 3 x 75 x
−2
−1
0
1
2
y
−3
2
⎛ 2 ⎞⎛ 5 ⎞
16. ⎜ 5 x 3 ⎟ ⎜ 6 x 2 ⎟
⎝
⎠⎝
⎠
21. Complete the table and graph: y = x 2 + 2
x
x
x+ y
⎛ 9x −5 y 4 ⎞
17. ⎜ −7 ⎟
⎜ x
⎟
⎝
⎠
3
2
18. (5 + 2i ) − ( −4 − 7i )
19.
(4 − i )
(3 + i )
20. Solve for x:
2 x + 5 = 3x − 3
y
22.
(a)
(b)
(c)
For the given graph, answer the following questions.
Is this a function?
What is the domain?
What is the range?
x
23. Given f ( x) = 2 x + 5 and g ( x) = x 2 + 2 , Compute the following. Simplify your answers:
(a) g ( −5)
(b) f ( a + h)
(c) g ( a )
24. Sketch the graph of 3 x + 4 y = 12 and find the intercepts.
25. Sketch the graph of x = 5
26. Find the equation of the line that passes through the points (−3, 2) and ( −5,10)
27. Find the equation of the line that is perpendicular to the line x + 3 y = 4 and passes through the point (4, 6) .
28. Find the equation of the line that is parallel to the line y = 6 and passes through the point (5,1) .
29. Graph the following: 4 x + 2 y ≤ 8
30. Graph the following: x > 5
31. Find the x-intercepts of the graph of y = 3x 2 + 5 x − 2
32. Solve 2( x + 3)( x − 2) = −4 using the quadratic formula.
33. Solve 5( x + 3)2 + 45 = 0 using the square root method (extraction of roots).
34. Solve x 2 + 6 x + 3 = 0 by completing the square.
35. Set up an equation and solve: The area of a rectangle is 40 sq. ft. The length is 2 ft. less than twice the
width. Find the dimensions.
36. Set up equations and solve: The sum of 2 numbers is 18. Their difference is 42. Find the numbers.
Answers
( 3x − y ) ( 9 x 2 + 3xy + y 2 )
1.
(b)
( −∞, ∞ )
[ −1, ∞ )
2. x (5 x − 2 y )( x + y )
3. ( x + 4)( x − 3)( x + 3)
(c)
4. 2 y 2 ( 3 x + 7 )( x − 2 )
23. (a) 27
(b) 2a + 2h + 5
(c) a 2 + 2
( x + 3)
5.
or −
−3
3x ( x + 2 )
6.
( x + 3)
3
24. y-intercept = 3
x- intercept = 4
( x + 4)( x − 3)( x + 1)
( )
x(x + y )
y y+x
7.
y
2
2
8. x = −12
9. x = 2 hours
10. 2 x3 y 3 2
x
11. 5 x3 y 4 2 xy
2 7
7
13. 35 x 3 x
x( x − y)
x − xy
or
14.
x− y
x− y
64
15.
125
12.
19
16. 30x
25.
y
6
17. 27 x3 y 6
18. 9 + 9i
11 − 7i
11 7
19.
or
− i
10
10 10
2
20. x = 2 x = is extraneous solution
9
y
21.
x
y
−2
6
−1
3
0
2
1
3
2
6
22. (a) yes
x
x
26. y = −4 x − 10
27. y = 3 x − 6
28. y = 1
y
29.
x
30.
Dashed/dotted line
y
x
31.
32.
33.
34.
35.
36.
⎛1 ⎞
⎜ , 0 ⎟ ( −2, 0 )
⎝3 ⎠
−1 ± 17
2
x = −3 ± 3i
x = −3 ± 6
length = 8 ft. width = 5 ft.
The two numbers are 30 and −12