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Title: Algebra _ Factorisation
Description: Algebra _ Factorisation Factorization using common factors To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is its factorization.
Description: Algebra _ Factorisation Factorization using common factors To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is its factorization.
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Algebra
Factorisation
Factorize the following:
1
...
x3 + 9x2 + 23x + 15
Solution:
1 + 9 + 23 + 15
0 ( x 1) is not a factor
1 + 23 = 9 + 15 = 24 (x 1) is a factor
1
1
0
9
1
23
8
15
15
1
8
15
0
x2 + 8x + 15 = (x + 3) (x + 5)
The factors are ( x + 1) ( x + 3) ( x + 5)
Factorize the following:
3
...
2x4 + 7x3 + x2 – 7x 3
Solution:
1
1
2 + 7 + 1 7 3
= 0
( x 1) is a factor
2 + 1 3 = 7 7
= 0
( x + 1) is also a factor
2
7
1
7
3
0
2
9
10
3
2
9
10
3
0
0
2
7
3
2
7
3
0
2x2 + 7x + 3 = 2x2 + 6x + x + 3
= 2x ( x + 3) + 1 ( x + 3)
= ( x + 3) (2x + 1)
The factors are ( x 1) ( x + 1) ( x + 3) ( 2x + 1)
Factorize the following:
5
...
m3 + 3m2 – 4m – 12
Solution:
1 + 3 4 12 0
(m 1) is not a factor
1 4 3 12 (m + 1) is also not a factor
In that case try m = 2
2
1
0
3
2
4
10
12
12
1
5
6
0
m2 + 5m + 6 = ( m + 2) (m + 3)
The factors are (m 2) ( m + 2) ( m + 3)
Factorize the following:
7
...
a3 – 5a2 – 2a + 24
1 5 2 + 24
1 2 5 + 24
Solution:
0 (a 1) is not a factor
1 (a + 1) is also not a factor
Try a = 2
2
1
0
1
5
2
3
2
6
24
16
8
8
( a 2) is not a factor
Try a = 2
2
1
0
5
2
2
14
24
24
1
7
12
0
a2 – 7a + 12 = ( a 3) ( a 4)
The factors are ( a + 2) ( a 3) ( a 4)
Factorize the following:
9
Title: Algebra _ Factorisation
Description: Algebra _ Factorisation Factorization using common factors To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is its factorization.
Description: Algebra _ Factorisation Factorization using common factors To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is its factorization.