A trinomial or quadratic expression takes the form **ax ^{2} + bx + c **where a, b and c are numbers.

In this worksheet, we will only consider cases when a = 1.

Sometimes it is not possible to factorise this expression into two brackets but, when it is, we can follow this method.

In x^{2} + bx + c we look for pairs of numbers which multiply to give c and add to give b.

**Example**

Factorise the following quadratic expression.

x^{2} + 7x + 12

**Answer**

x^{2} + 7x + 12

Here we have b = 7 and c = 12.

So we list the factor pairs of 12 and see which pair adds to give 7.

Factor Pairs | Sum of factors |
---|---|

1 and 12 | 13 |

-1 and -12 | -13 |

2 and 6 | 8 |

-2 and -6 | -8 |

3 and 4 | 7 |

-3 and -4 |
-7 |

We now split the middle term 7x using the chosen factor pair i.e. 3x and 4x

x^{2 }+ 3x + 4x +12

Consider the expression in pairs

x^{2} + 3x + 4x + 12

Factorise each pair

x (x + 3) + 4 (x + 3)

Combine

(x + 4) (x + 3)

This is the full factorisation

**(x + 4) (x + 3)**