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)`