Factorise quadratic expressions
Quadratic expressions have the general form:
ax^{2} + bx + c
They can often be factorised, usually into a pair of brackets.
For example:
x^{2} + 5x + 6 = (x + 2)(x + 3)
For factorising expressions like the one above, the process is fairly simple.
1) List all the factor pairs of c, in this case
1 2 3 6
2) Find a pair that sum to give b. In this example, 2 + 3 = 5. Then write out the pair of brackets using those two numbers.
[The reasoning behind this method is very simple, when we expand quadratic equations and we multiply the two numbers within the brackets it gives us the last number in the equation. So when we want to do the opposite and factorise a quadratic equation we simply do the opposite and find the factors which allow us to reach our last number.]
Let's try one more example of factorising a quadratic so we can make sure we have got this! Remembering the general form of Quadratic equations: ax^{2} + bx + c
x^{2 }+ 9x + 14 = ?
Firstly we should write down all the factors of c (14):
1, 2, 7, 14
Then we can pick the pair that gives us the sum of b (9):
2 + 7 = 9
Now all we must do is put these two numbers into our brackets and we have succesfully factorised our quadratic equation;
x^{2 }+ 9x + 14 = (x + 2) (x + 7)
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