Question

How do you factor ##?

Answer 1

1. Find two numbers that multiply to give ac (in other words a times c), and add to give b.
2. Rewrite the middle with those numbers.
3. Factor the first two and last two terms separately

Explanation:

`x^2+4x-12`
`6*-2=-12`
6-2=4

Answer= `(x+6) (x-2)`

Answer 2

Factoring can involve many different things at different stages..

Firstly.. you'll be taught how to factorize when all the terms have something in common
For example
Factorize `12+36x`
Prime factorize them
`12=color(red)2xxcolor(red)2xxcolor(red)3`
`36=color(red)2xxcolor(red)2xxcolor(red)3xx3xx x`
#12+36x=12(1+3x)

Then.. you'll be taught how to factorize using rules of factorising
Rules:
`(a+b)^2=a^2+2ab+b^2`
`(a-b)^2=a^2-2ab+b^2`
`(a+b)(a-b)=a^2-b^2`
`(x+a)(x+b)=x^2+(a+b)x+ab`

For example
Factorize

`16-a^2+2ab-b^2`

`16-(color(red)(a^2-2ab+b^2))`

Remember the rule?

You get

`16-(a-b)^2`

Now..

`16=4^2`

You get

`4^2-(a-b)^2`

remember the rule?
`a^2-b^2=(a+b)(a-b)`

You get

`(4+(a-b))(4-(a-b))`

Expand

`(4+a-b)(4-a+b)`

Then will come splitting the middle term to factorize...

This video will teach you

Then will come harder laws(rules)
Like
`(a+b+c)^2+a^2+b^2+c^2+2ab+2bc+2ca`