How do you factorise expressions?

Answer 1

If you are factorising expressions you need to look for the highest common factor (hcf);

for example

15y + 10 = 5(3y+5)

hcf = 5

(5 x 3y = 15y) + (5 x 2 = 10)

(5 x 3y) + (5 x2)

Put the hcf at the beginning of the equation!

5(3y+5)

However if you are factorising quadratic expressions the method is similar but slightly similair. You need to find the factors of the last number that will make the sum of the middle number. I know your thinking it's difficult but once you know how to do it, it's easy!

p2 - 8p + 15 = (p-3)(p-5)

1. Find the factors of 15

15 x 1

3 x 5

2. Find the two which will sum up to 8

3 x 5

3. Use the squared number/letter in the expression

(p-3)(p-5)

It can get harder be aware, so if you need more help I suggest youu search the internet.

Answer B

Just to correct that the above answer is wrong for factorising 15y + 10.

The answer is 5(3y + 2). You have added 5 and 5 instead of timesing 5 and 2 which should give 10.

Also the example that you gave for p2 - 8p + 15 = (p-3)(p-5) wasn't correct but the answer was.

1. Firstly we find the factors of 15 such as:

5x3

15x1

-5x-3

these all equal to 15.

2. Then we find the factors of 15 that add up to -8

which are -5 and -3

3. Now we put it all together. P² will set up as (p )(p ) this means p² in expanding brackets.

Now it becomes: (p-5)(p-3) if we expand this answer which is doing the opposite of factorising, the answer will become back to p2 - 8p + 15.