Factorise 𝑥 squared minus 𝑥 minus
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.