Ok, so factorising is the opposite of expanding - you put the expression back in the brackets! (This can be used to solve quadratic equations later on).
Right, so here's the question:
Fully factorise the expression x2 + 7x + 12.
There are a few simple rules to remember:
1. If there is more than 1 in front of the x2 term, this changes the way you factorise. More on this in another post.
2. The SUM of the numbers in each bracket equals the number in front of the x term (7).
3. Multiplying the numbers in each bracket gives the number (12).
So, we know each bracket starts with an x (there's no other way to get x2):
(x )(x )
We also know that both numbers must be positive, since both 7 and 12 are.
(x + )(x + )
So, now we need 2 numbers that add up to 7 and multiply to 12. First, we find all possible numbers that multiply to 12 (factors of 12):
1 x 12
6 x 2
4 x 3
Well, 1 and 12 add up to 13, not 7.
6 and 2 add up to 8.
4 + 3 = 7.
Ok, so we know it's 4 and 3! Now:
(x + 4)(x + 3)
Another post soon on how to use this to solve quadratics! Try our quiz to test yourself on this:
Comments