- Method 1: Use a calculator to solve the quadratic expression equal to 0
- If the solutions are integers or fractions (without square roots), then the quadratic expression factorises

- Method 2: Find the value under the square root in the quadratic formula,
*b*^{2}– 4*ac*(called the discriminant)- If this number is a perfect
**square number**, then the quadratic expression factorises

- If this number is a perfect

- Does it have
**2 terms only**?- Yes, like
- Use "basic factorisation" to take out the highest common factor

- Yes, like
- Use the "difference of two squares" to factorise

- Yes, like
- Does it have
**3 terms**?- Yes, starting with
*x*^{2}like- Use "factorising simple quadratics" by finding two numbers that add to -3 and multiply to -10

- Yes, starting with
*ax*^{2}like- Check to see if the 3 in front of
*x*^{2}is a**common factor**for**all three****terms**(which it is in this case), then use "basic factorisation" to**factorise it out**first - The quadratic expression inside the brackets is now
*x*^{2}+... , which factorises more easily

- Check to see if the 3 in front of
- Yes, starting with
*ax*^{2}like- The 3 in front of
*x*^{2}is not a - Use "factorising harder quadratics", for example factorising by grouping or factorising using a grid

- The 3 in front of

- Yes, starting with

Factorise .

Spot the common factor of -4 and put outside a set of brackets, work out the terms inside the brackets by dividing the terms in the original expression by -4.

Check the discriminant for the expression inside the brackets, , to see if it will factorise.

, it is a perfect square so the expression will factorise.

Proceed with factorising as you would for a harder quadratic, where .

"+12" means the signs will be the same.

"-25" means that both signs will be negative.

The only numbers which multiply to give 24 and follow the rules for the signs above are:

and and and

but only the first pair add to give .

Split the term into .

Group and factorise the first two terms, using as the highest common factor and group and factorise the last two terms using as the highest common factor.

These factorised terms now have a common term of , so this can now be factorised out.

Put it all together.

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