How do you factor ##?

2 Answers
May 18, 2018

Answer:

  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)#

May 18, 2018

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#