Review for Exam #1
Math 10 Fall 2012
For attendance, turn in solutions to any two of the problems marked with a *.
Chapter 5
1. Simplify the following expressions:
58 · 37
53 · 35
(b) 200y 0 − (200y)0
5
−2a8
(c)
b3
(a)
(d)
−15x16 y 2
45x2 y 2
2. Divide each polynomial by the respective polynomial:
10x3 − 20x2
−5x
25x8 − 50x7 + 3x6 − 40x5
(b)
−5x5
3
2
2y − y + 3y + 2
(c)
(Use long division)
2y + 1
(a)
3x5 − x3 + 4x− 12x − 8
x2 − 2
5
3
x +x −2
(Use synthetic division) *
(e)
x−1
(d)
3. Divide each of 5x8 − 20x5 + 10x2 and 14x5 y 3 + 42x4 y 5 − 98xy 2 by their respective greatest common
factors.
Chapter 6
1. Completely factor the following polynomials:
(a) 6x3 + 24x
(b) 3r3 − 27r2 − 210r
(c) 20y 2 + 12y + 1
(d) y 5 − 16y
(e) 2y 5 − 128y 2
(f) 100y 2 + 49
(g) 10a4 b2 − 15a3 b3 − 25a2 b4
(h) x2 + 14x + 49 − 16a2
(i) 12y 3 + 16y 2 − 3y − 4 *
(j) (y + 1)3 + 1
1
2. Solve the following equations using factoring:
(a) x2 + x − 42 = 0
(b) x2 = 8x
(c) 9x2 = 30x − 25
(d) y 3 + 2y 2 = 3y
(e) (x − 4)(x − 5) + (2x + 3)(x − 1) = x(2x − 25) − 13
(f) (x − 3)2 + 2(x − 3) − 8 = 0 *
3. The formula
S = 2x2 − 12x + 82
models spending by international travelers to the United States, S, in billions of dollars, x years after
2000. In which years did international travelers spend $72 billion? $66 billion?
4. Great white sharks have triangular teeth with a height that is 1 centimeter longer than the base. If the
area of one tooth is 15 square centimeters, find its base and height. (Hint: Area = 12 ×Base×Height)
Chapter 7
1. Find all values of the variable for which each rational expression is undefined:
y+8
6y 2 − y − 2
y−6
(b) 2
y − 36
(a)
2. Simplify each rational expression:
(a)
(b)
(c)
(d)
(e)
3x − 9
6x
x2 − 12x + 36
4x − 24
2
3y + 4y − 4
6y 2 − y − 2
y 2 − 7y + 12
3−y
3
x − 3x2 + 9x
*
x3 + 27
3. Perform the following operation(s):
(a)
(b)
(c)
(d)
(e)
9y + 21 y − 2
·
y 2 − 2y 3y + 7
x2 + 6x + 9
1
·
x3 + 27
x+3
x2 + x
x2 − 1
÷
*
x2 − 4 x2 + 5x + 6
x2 − 4y 2
x2 − 4xy + 4y 2
÷
x2 + 3xy + 2y 2
x+y
2
2
5x − x
6x + x − 2 2x2 − x − 1
÷
·
3x + 2
10x2 + 3x − 1
2x2 − x
2