How Large Is One Zillion? - Diwa Learning Systems

Answers to Exercises
How Large Is One Zillion?
Exercise 1
A. Factoring
xm xn = xm–n , x ≠ 0
Addition of Integers
x –n = 1
xn , x ≠ 0
( x
y ) n
= xn
y n
(xm ) n
= xmn Expanding the power
B. Expressing numbers in terms of
exponents
Exercise 2
(xm ) n
= xmn and x0 = 1, x ≠ 0
x m · x n = x m+n
Addition of integers
x –n = 1
x n , x ≠ 0 and x 0 = 1, x ≠ 0
1 2 3 4 5
0 1 6 8 9 4
6 7
. 3 2 . 8 1
8 9 10
0 2 0 2 4 0
12
11
0 4 4 8 0
0 1 4 4 0
13 14
0 1 1 3 0
15 16 17
0 8 1 2 0 0
18 19 20
4 3 . 3 0 0
21 22
1 0 6 4 4 0
Factor In
Answer to the Preliminary Problem:
0, one of the factors is (x – x) = 0
TATSULOK Second Year Vol. 11 No. 3 e-Pages
I.
1. Factor = 3ab (a2 – 3ab + 9b) 2
2. Factor = (m – n)(3m – 1)
3. Factor = 4(u – 1)(2 – v)
II.
(1) To factor x2 + 5x + 6, I need two numbers that add
up to 5 and have a product of 6.
Thus, x2 + 5x + 6 = (x + 5)(x + 1).
(2) To factor x2 – 2x – 3, I need two numbers that add
up to –2 and have a product of –3.
Thus, x2 – 2x – 3 = (x – 3)(x + 1).
(3) To factor x2 – 8x + 15, I need two numbers that
add up to –8 and have a product of 15.
Thus, x2 – 8x + 15 = (x – 3)(x – 5).
III.
1. (x + 7) and (x + 4)
2. (x + 3) 2
3. (x + 4) and (x – 1)
4. (4x – 1) and (3x – 4)
5. a b
c
d
8