Video: Pack 2 • Paper 3 • Question 8

Pack 2 • Paper 3 • Question 8

01:55

Video Transcript

Factorise 𝑥 squared minus 𝑥 minus six.

We will start by writing down the factors of negative six. We have negative one and six, one and negative six, negative two and three, and two and negative three. Now we need to find a factor pair which sum to give the coefficient of the 𝑥 term.

In our expression, the 𝑥 term is negative 𝑥. And so the coefficient of the 𝑥 term is negative one. So we need to find a factor pair which sums to give negative one.

Now we spot that two plus negative three is equal to negative one. And so therefore our factor pair which sums to give negative one is two and negative three. And therefore, we can factorise 𝑥 squared minus 𝑥 minus six: 𝑥 plus two timesed by 𝑥 minus three.

We’re able to quickly check this answer by expanding the brackets. Using the FOIL method, we can start by multiplying the first terms from each bracket. So that’s 𝑥 timesed by 𝑥, giving us 𝑥 squared. Then the outside terms, so that’s 𝑥 timesed by negative three, which gives us minus three 𝑥. Then we multiply the inside terms. So that’s two timesed by 𝑥, giving us plus two 𝑥.

And finally, we multiply the outside terms in each bracket. So that’s two timesed by negative three, which gives us negative six. And this is also equal to 𝑥 squared minus 𝑥 minus six, which is exactly the same as the expression we were factorising. And so therefore we can be sure that our answer was correct.

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