Page 117 - Start Up Mathematics_8 (Non CCE)

4
3 2
-24xy z
4 3 2
2 2
(b) –24x y z ÷ 4x y = = –6 × x 4 – 2 × y 3 – 2 × z 2
4xy 2
2
2
2
2
= –6 × x × y × z = – 6x yz 2
53 4
-52ab c
3
5 3 4
2
(c) –52a b c ÷ (–2a bc ) = = 26 × a 5 – 3 × b 3 – 1 × c 4 – 2
3
-2abc 2
2 2 2
2
2
2
= 26 × a × b × c = 26a b c
l Every monomial consists of one term but a single term may not always be a monomial.
l Multiplication of monomials results in a monomial but division of a monomial by another monomial may
not result in a monomial.
32
12xy 4x 2
2
-
-
For example, =4x 31 y 24 =4xy - 2 = (not a monomial)
3xy 4 y 2
EXERCISE 6.2
1. Divide the following:
6 4
4 5
8 6 3
3 3
2 3
9 7
(a) 14x y z by 7x y (b) 20x y z by 4x y z (c) –105a b by 5a b
10 7 6
6 3 2
2 3 4
2 3
2 2
4 5 2
(d) 152a b c by –8b c (e) –88p q r by –11p q (f) –78p q r by 13p q r
2. Simplify:
4
3 2
88 8
11 94 3
160xy zu -96xy z -125ab cd 3 82abc
54 2
(a) (b) (c) (d)
22
5
3
2
45 3
4xy zu 2 16xyz -5abcd 2ab c
Division of Polynomials
Division of a polynomial by a monomial
Step 1: The polynomial is the dividend and the monomial is the divisor.
Step 2: Arrange the terms of the dividend in descending order of their degrees.
3
3
2
2
For example, 5x + 2x – 6 + 3x is written as 3x + 5x + 2x – 6.
Step 3: Divide each term of the polynomial by the given monomial using the rules of division of a monomial
by a monomial.
3
5
2
5
6
4
8
Example 2: Divide: (a) 15x + 12x – 9x + 6 by 3 (b) 32x – 24x + 16x – 12x by 4x 2
2
5
4
5
2
4
Solution: (a) (15x + 12x – 9x + 6) ÷ 3 = 15x + 12x - 9x + 6 = 15x 5 + 12x 4 - 9x 2 + 6
3 3 3 3 3
2
4
5
= 5x + 4x – 3x + 2
6
5
8
8
6
2
5
3
(b) (32x – 24x + 16x – 12x ) ÷ 4x = 32x - 24x + 16x - 12x 3
4x 2
32x 8 24x 6 16x 5 12x 3
= - + -
4x 2 4x 2 4x 2 4x 2
Ê x m ˆ
-
= 8x 8 – 2 – 6x 6 – 2 + 4x 5 – 2 – 3x 3 – 2 Á  n = x mn ˜ ¯
Ë
3
4
6
= 8x – 6x + 4x – 3x x
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