Factorization 2
Mathematics J.S.S 3 Second Term
Theme: Algebraic Process
Sub Theme: Algebraic Operation
WEEK 2
Factorization 2
Performance Objectives
Students should be able to;
- Solve word problems involving factorization
- Solve simple equations involving factorization
- Factorize completely
Word problems involving factorization
Content
Examples
- The sum of a number and its square is 72. Find the number.
Solution
Let x be a number
x2 + x = 72
x2 + x – 72 = 0
(x + 9)(x - 8) = 0
x + 9 = 0 or x - 8 = 0
x = -9 or x = 8
The number is -9 or 8.
2. If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the number.
Solution
Let x +ve number
(x + 5)2 = 12x + 88
x2 + 10x + 25 = 12x + 88
x2 - 2x - 63 = 0
(x - 9)(x + 7) = 0
x - 9 = 0 or x + 7 = 0
x = 9 or x = -7
The number is 9.
3. The sum of two numbers is 12 and the sum of their squares is 80. Find the numbers.
Solution
* Let x 1st number
x2 + (12 - x)2 = 80
12 - x 2nd number
x2 + 144 - 24x + x2 = 80
2x2 - 24x + 64 = 0
x2 - 12x + 32 = 0
(x - 8)(x - 4) = 0
x - 8 = 0 or x - 4 = 0
x = 8 or x = 4
The numbers are 4, 8.
4. The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96 sq. cm. Find its dimensions.
Solution
* Let x width and x + 4 length
x(x + 4) = 96
x2 + 4x = 96
x2 + 4x - 96 = 0
(x + 12)(x - 8) = 0
x = -12 or x = 8
The dimensions are: width 8 cm, length 12 cm
5. One number is 3 more than another. The sum of their squares is 149. Find the numbers.
Solution
* Let x 1st number and x + 3 2nd number
x2 + (x + 3)2 = 149
x2 + x2 + 6x + 9 = 149
2x2 + 6x - 140 = 0
x2 + 3x - 70 = 0
(x + 10)(x - 7) = 0
x + 10 = 0 or x - 7 = 0
x = -10 or x = 7
The numbers are: -10, -7 or 7, 10
6. The sum of the squares of two consecutive positive even integers is 340. Find the integers.
Solution
* Let x +ve number and x + 2 +ve number
x2 + (x + 2)2 = 340
x2 + x2 + 4x + 4 = 340
2x2 + 4x - 336 =0
x2 + 2x - 168 = 0
(x + 14)(x - 12) = 0
x + 14 = 0 or x - 12 = 0
x =-14 or x = 12
The numbers are 12, 14