How To Factorise into Single Brackets

Factorising means putting the algebraic expression back into brackets. You will have already studied expanding brackets. Factorising is the reverse process. You will have already learnt how to simplify algebraic expressions. In the example below we see that 7x + 14 when factorised into single brackets is 7(x + 2). Once you successfully factorise an expression, you can check the answer by expanding the brackets.

What Is Factorising Into Single Brackets?

Factorising examples below including 2x + 6, 7x + 42, 10x - 5, 48 + 96x. When factorised 2x + 6 equals 2(x + 3), 7x + 42 equals 7(x + 6), 10x - 5 equals 5(2x -1), 48 + 96x = 12(4 + 8x). The questions factorise into single brackets.

How Do You Factorise Quadratic Equations?

Once you learn how to factorise expressions into single brackets, students learn how to factorise quadratic expressions. Quadratic expressions have its highest power as two. Quadratic expressions usually begin with x², or there may be a coefficient before x², such as 6x² + 5x + 1, in this case 6 is the coefficient before x². The example below shows how to factorise the expression x² + 11x + 24 using a grid method.

Factorising Quadratic Equations Question 1

The example below factorising x² + 11x + 24 using a grid method. We find two numbers that multiply to get 24 and add together to make 11. The numbers are 3 and 8. The final answer is (x + 8)(x + 3).

Factorising Quadratic Equations 2

Factorising question 2 factorises x² - 5x - 84. We find two numbers that multiply to make - 84 (negative number), that also total together to make - 5 (negative five).  The final answer is (x - 12)(x + 7). We check the answer by expanding the brackets.

Factorising Into Double Brackets - Question 3

Factorising questions below factorise (x + 1)(x + 3), (x - 4)(x + 3) and (3x - 2)(x + 2). This is the practice of factorising into double brackets.