Factorising a quadratic expression, such as `x^2 + 6x + 8`, means putting the brackets back to obtain an expression with two sets of brackets: `(x + 4)(x + 2)`.

For the expression `x^2 + 6x + 8`, the numbers in the brackets must multiply together to make 8 (the number at the end of the expression).

At the same time the numbers in the brackets must add together to make 6 (the number in front of the `x`).

So what two numbers, when multiplied together make 8; and when added together make 6?

To factorise a quadratic:

what are the combination of factors that make the number value, and

which pair of factors also add up to the coefficient of the `x` term?

Negative signs have to be taken into account when determining the factors. remember that two negatives multiplied together give a positive result.

Factorising a quadratic is the opposite process to expanding aa binomial.

Factorise `x^2 + 13x + 42`

The numbers for the brackets multiply together to make 42; and add together to make 13:

factors of 42 | added | |

1 and 42 | 43 | |

2 and 21 | 23 | |

3 and 14 | 17 | |

6 and 7 | 13 | `larr` |

Answer: `(x + 6)(x + 7)`

Factorise `a^2 - 8a + 15`

The numbers for the brackets multiply together to make 15; and add together to make -8:

factors of 15 | added | |

1 and 15 | 16 | |

3 and 5 | 8 | |

-3 and -5 | -8 | `larr` |

-1 and -15 | -16 |

Answer: `(a - 3)(a - 5)`

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