Question

`24x+16` how do you factorise fully ?

Answer 1

`8(3x+2)`

Explanation:

Finding the highest common factors that go into both numbers:

Factors of `24`:

`24 and 1`
`12 and 2`
`8 and 3`
`6 and 4`

Factors of `16`:

`16 and 1`
`8 and 2`
`4 and 4`

As we can see, `8` is the HCF (highest common factor) in both numbers, so we factor this outside the bracket.

`rArr 8(...+...)`

`therefore` `8` needs to multiply into `24x` and `16`

`rArr 8 xx 3x=24x`

`rArr 8 xx 2=16`

`therefore` `rArr 8(3x+2)=24x+16`

Answer 2

`8(3x+2)`

Explanation:

`"take out a "color(blue)"common factor "8`

`=8(3x+2)`

Answer 3

`8(3x+2)`

Explanation:

Find the common factors of `24` and `16` (numbers that multiply to give `24` and `16` respectively):

`24: 1, 2, 3, 4, 6, 8, 12, 24`
`16: 1, 2, 4, 8, 16`

Then find the highest common factor of `24` and `16` which is `8`.

Take 8 to be on the outside of the bracket as this will be the number the terms would be multiplied by to give `24x` and `16`. Divide each term by `8` and you should get:

`8(3x+2)`

This is the fully factorised form of `24x+16`.