Factorising Quadratics
Maths: Edexcel IGCSE Higher, topic 2.1.5
Factorising Quadratics
A quadratic expression is of the form ax2 + bx + c where a, b and c are numbers. For example 2x2 + 3x - 1.
Factorising
- Factorising a quadratic expression means writing it as the product of two brackets.
Difference of two squares
- When a quadratic expression is the difference of two squares it can be easily factorised:
- General case: a2 - b2 = (a + b)(a - b).
Factorising Quadratics
We can factorise quadratics in the form ax² + bx + c when a = 1.
To factorise x² + 2x - 8:
Find pairs of numbers which multiply to give (-8)
Select the pair which also adds to give 2
These numbers multiply to give (-8) and add to give 2
Write these two numbers in the brackets
Check your answer by expanding the brackets
Completing the Square
Completing the square for y = 2x2 + 12x + 5:
Write the equation
Factor out the x² term
Half the x coefficient and put it in the bracket like this
Expand
We need to minus 13 from the red equation to get the purple
Test yourself on Factorising Quadratics
Which of these is an example of difference of two squares?
Which of these is an example of difference of two squares?
Which of these is an example of difference of two squares?
Which is the correct factorisation of this expression?
x² + 3x + 2x² - 3x - 4Which of the following is NOT a correct factorisation of this expression?