Page 74 - Mathematics_Form_Two

Algebra

Factorisation of quadratic expressions a = 2, b = and c = . So
6
7
Factorisation is the process of writing
an expression as a product of its factors. ac = 2 6 12= .
Numbers and algebraic expressions can Find the pair of factors of 12 whose
be expressed in terms of factors. sum is 7.
For instance, 10 can be expressed as a The pairs of factors of 12 are
FOR ONLINE READING ONLY
Mathematics for Secondary Schools The expression x −− 3),. That is, The sum of 1− and 12− is 12−
product of 2 and 5 or 1 and 10.
The sum of 1 and 12 is 13
2
12 can be
x
expressed as a product of two linear
The sum of 2 and 6 is 8
4) and (x +
factors (x −
2
4)(x +
x −−
−
3).
12 (x=
x
The sum of 2− and 6− is 8−
Quadratic expressions can be factored
using three main methods which are The sum of 3 and 4 is 7
The sum of 3− and 4− is 7−
splitting the middle term, difference of
two squares and perfect squares. Therefore, the correct choice is 3 and 4.
So the terms are 3x and 4x.
Factorisation by splitting the middle 2x + 2 7x + 62x= 2 + 4x + 3x + 6
term = (2x + 2 4 ) (3x + x + 6)
Factorisation by splitting the middle = 2 (xx + 2) 3(x+ + 2)
term involves the splitting of the middle = (x + 2)(2x + 3)
term into two terms. For instance, in the
2
quadratic expression ax + 2 bx + , c the Therefore, 2x + 7x + 6 (x= + 2)(2x + 3).
middle term is bx. To split the middle
term, the following steps can be used: Example 4�17

(i) Find two numbers whose sum is equal Factorize 6x 2 11x - + 4 by splitting the
to b and whose product is equal to ac.
(ii) To find the two numbers in (i), list all middle term.
the factors of ac and determine a pair Solution
whose sum is b. Since ac = 24 and b = − 11, find a pair of

factors of 24 whose sum is –11.
Example 4�16
The pairs of factors of 24 are: –1 and

Factorize the expression 2x + 2 7x + 6 by –24, –2 and –12, –3 and –8, –6 and – 4.
splitting the middle term. Therefore, the correct choice is –3 and –8
Solution since –3 + –8 = –11 and (–3) × (–8) = 24.

The coefficients are 2, 7 and the Thus, 11x- 3x = - 8x - .

constant term is 6. That is, It follows that,

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Student's Book Form Two

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