How do you factor ##?

Question

Julia Adams · Accepted Answer

Find two numbers that multiply to give ac (in other words a times c), and add to give b.
Rewrite the middle with those numbers.
Factor the first two and last two terms separately #x^2+4x-12# #6*-2=-12# 6-2=4 Answer= #(x+6) (x-2)#

Abigail Allen · Answer

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#

Genesis Allen · Answer

undefined To factor an expression means to rewrite it as a product of its factors. The specific method for factoring depends on the type of expression you have. Some common techniques for factoring include factoring by grouping, factoring quadratics using the AC method or the quadratic formula, factoring the difference of squares, and factoring trinomials using methods such as trial and error, decomposition, or the quadratic formula. If you provide the expression you want to factor, I can give you a more specific explanation tailored to that expression.