Maths Hacks: Video playlist

Factorising quadratic expressions.

These can be tough, but use this method to minimise losing marks.

The trick with this one is to always double check your answer by multiplying out the brackets and comparing your answer with the original expression you started with.

For example, take the expression 𝑥 squared plus 7𝑥 plus 10. The correct way to find the bracket values is to find two factors of the constant 10, so, two numbers which multiply together to give 10, that also add up to the coefficient of 𝑥, which is 7.

The factors of 10 are 10 and 1, or 5 and 2. As you can see, only one of these pairs adds up to the 𝑥-coefficient 7: 5, and 2. To check your answer is correct, substitute these values into the brackets: 𝑥 plus 2 and 𝑥 plus 5 and multiply out.

Here we’ll use the grid method, but you could use any method that you feel comfortable with.

So, multiplying the terms together gives us 𝑥 times 𝑥 which equals 𝑥 squared, 𝑥 times 2 which equals 2𝑥, 5 times 𝑥 which equals 5𝑥, and 5 times 2 which equals 10.

Add all these values together and we have 𝑥 squared plus 7𝑥 plus 10. Notice this is the original expression and shows that the factorisation is correct. But a common mistake in factorising is picking any two factors that multiply to give the constant, like 1 and 10 for 10, and assuming the expression can be written as 𝑥 plus 1, 𝑥 plus 10.

It seems logical because 1 times 10 does equal 10, but factorising isn’t just about multiplication. Remember, the numbers also need to add up to match the 𝑥-term coefficient, which in this example is the middle term 7𝑥. If we made this mistake, let’s see what happens when we multiply out the brackets to check our answer.

Multiplying the terms together gives us 𝑥 times 𝑥 which equals 𝑥 squared, 1 times 𝑥, which gives us 1𝑥 or just 𝑥, 10 times 𝑥 gives us 10𝑥, and finally 1 times 10 gives us 10. Adding up the like 𝑥 terms leaves us with 𝑥 squared plus 11𝑥 plus 10.

As you can see, this isn’t the same as the original expression. This is why it’s really important when factorising quadratics to remember two things.

One: multiply out the brackets to check your answer and two: compare your answer to the original expression you started with. If it matches, then you’ve conquered factorising quadratics.