Factorisation of Quadratic Expressions (Chap 3.3)

Factorisation of Quadratic Expressions using a Multiplication Frame

a) Example: x² + 8x + 12

Step 1: Write x² in the top-left corner and 12 in the bottom-right corner of the multiplication frame.

Step 2: Consider the factors of x²  and 12. Write them in the first column and the first row.

Step 3: Multiply them to complete the multiplication frame and check whether the result matches the given expression.

Therefore, x²  - 5x + 4 = (x-1)(x-4)

b) Example: 3x²  + 7x -6 

Therefore, 3x²  + 7x - 6 = (3x - 2)(x + 3)

c) Example: 4x² - 6x - 4 = 2(2x² - 3x -2)  

extract the common factor 2

Therefore, 4x² - 6x - 4 = 2(2x + 1)(x - 2)

The general form of a quadratic expression in one variable is:

 ax² + bx + c,
where x is the variable, a, b and c are constants and a ≠ 0.

Example : x² - 2x -8

Step 1: Write x² in the top-left corner and -8 in the bottom-right corner of the multiplication frame.

Step 2: Consider the factors of x² and -8. Write them in the first column and the first row.

Step 3: Multiply them to complete the multiplication frame and check whether the result matches the given expression. 

Therefore, x² - 2x - 8 = (x + 2)(x - 4)

Video link: http://education-portal.com/academy/lesson/factoring-quadratic-equations-practice-problems.html#lesson