MAT 104 Worksheet 1
September 1, 2004
1. Factor each of the following integers into a product of prime numbers.
(a) 12 = 22·3
(b) 120 = 23·3·5
(c) 1024 = 210
2. Indicate the set {x|x < 2}on the number line below.
0-1-2-2-4-5 1 2 3 4 5
3. Write the following numbers from smallest to largest. |−3|,−7, |−7|,−3.
−7−3|−3|= 3 |−7|= 7
4. Evaluate each of the following expressions.
(a) 4 −6 + 3 = −2 + 3 + 1
(b) √9 + 3
√64 + 4
√16 = 3 + 4 + 2 = 9
(c) 1
2+1
3=3
6+2
6=5
6
5. Simplify each expression.
(a)
¡x2¢3=¡x2¢ ¡x2¢ ¡x2¢
= (x·x) (x·x) (x·x)
=x6
(b) x2·x3= (x·x) (x·x·x) = x5
(c)
(x+y)2= (x+y) (x+y)
= (x+y)x+ (x+y)y
=x2+xy +xy +y2
=x2+ 2xy +y2
