Question

Factor completely: 2x +11x +12?

Answer 1

(2x+3)(x+4)

Explanation:

If you mean:

`2x+11x+12`

This simplifies to:

`13x+12`

Which factors to:

`-> 1(13x+12)` as nothing is common between the two terms apart from `1` of course...

If you mean `2x^2+11x+12`

Multiply the coefficient by the constant:

`2 xx 12=24`

We are trying to find a pair of numbers that add to make `11` and multiply to make `24`. Start out by listing the factors of `24`

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

By looking at these pairs we can conclude that `8+3` makes `11`, so we use these.

As all terms are positive, all numbers have to be positive

Plugging back in:

`2x^2+8x+3x+12`

Notice that we use the original +12, we only multiply to find the values to factor

Factor the two first terms:

`2x^2+8x -> 2x(x+4)`

Factor out the last two terms:

`3x+12 -> 3(x+4)`

`therefore` `2x^2+8x+3x+12 -> 2x(x+4)+3(x+4)` <-## Notice these brackets are the same

One bracket is (x+4), the other is the remaining terms which is `(2x+3)`

`-> (x+4)(2x+3)`

We can always expand to check:

`2x xx x=2x^2`

`x xx 3 =3x`

`4 xx 2x=8x`

`4 xx 3=12`

`-> 2x^2+8x+3x+12 -> 2x^2+11x+12`

Therefore this is factorised correctly.