Page 75 - Mathematics_Form_Two

Algebra
4 6x
So that, 6x 2 11x - += 2 3x - 8x - + 4
4 6x
So that, 6x 2 11x - += (6x= 2 2 3x - 3 ) (8x - x - 8x - + 4 - 4) So that, x + 2 6x + 9 = x + 2 3x + 3x + 9
4)
(6x= (6x= 2 2 3 ) (8x - 3 ) (8x - x - x - - - 4) = (x + 2 3 ) (3x + 9)
x +
+
2
= (6x= 3 (2 -- - 4) 1) = ( xx + 3) 3(x + 3)
x - xx
3 ) (8x - 1) 4(2x -
-
1) 4(2x -
xx 1)(3x -
= (2x = 3 (2 -- 4) 1) = (x + 3)(x + 3)
Therefore, (2x = 1)(3x - - 4) = (x + 3) 2
6x 2 11x - 4 (2x += 1)(3x- - 4).
Thus, the quadratic expression has
two factors which are identical
Example 4�18 2 2
x + 6x += 3) .
9 (x +
Factorize 2x 2 x + - 10 by splitting the Mathematics for Secondary Schools
middle term. Therefore, the playing ground is a
square of length (x + 3) m.
Solution
The correct choice of the pair of
factors of –20 is – 4 and 5; Thus, Exercise 4�4

x 4x = - 5.x + In questions 1 to 9, factorize the
So that, expressions by splitting the middle term:
2
2
So that, 2x FOR ONLINE READING ONLY
1.
10
10
-
5x+
4x-
x + -
2x=
x +
2
3x +
2
(2x = 2 4 ) (5x - x + - 10) 2. 6y + 2 11y + 4
= 2 (xx - 2) 5(x+ - 2)
= (x 2)(2x - + 5) 3. 2x − 2 17x + 8
Therefore, 4. y − 2 7y + 6
2x 2 x + - 10 (x = - 2)(2x + 5). 5. 3 2 2 d - 8d -
6. 35a− + 2a 2
Example 4�19
A building company is designing a 7. c − 2 18c + 45
rectangular playing ground whose 8. 12x + 2 27x − 39
total area is defined by the expression 9. x − 2 7xy + 12y 2

x + 2 6x + 9 ,where x in metres is the length
of playing ground. Deduce the possible 10. Maria wants to design a garden
dimensions of the playing ground. and needs to create a rectangular
flower bed with dimensions that fit
a specific area. The area of the bed
Solution can be modeled by the quadratic
2
2
The correct choice of the pair of factors expression 3y − 11y + 10 m .
of 9 is 3 and 3. Thus, 6x = 3x + 3.x Determine the possible lengths of
the sides of the flower bed.

69
Student's Book Form Two

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MATHEMATIC F2 v5.indd 69
MATHEMATIC F2 v5.indd 69 11/10/2024 20:11:54