How does factorization work with equations?

Question

I forgot how to do factorization when it comes to equations. I know how to do expansion, but I'm not sure how to do factorization. For example, how would you factorize:

6m - 2 (the m is a variable)

I'm not sure how to do the steps.

Thanks in advance =)

Answer 1

2(3m-1)

Answer 2

common factor of 6 and 2 is 2

2(3m - 1)

Answer 3

all factoring is is simplifying an equation or expression down to simpler parts that, when multiplied together give the original equation.

6m-2 can be factored to 2(3m-1) factoring out a 2.

There is not just one way to factor something, it depends on what you are working with.  For example x^2-3x could be factored down to x(x-3).  This is useful because it becomes much easier to see what the "zeros" of the problem are.  What I mean by that is it becomes much easier to see what x could make the entire expression equal zero.  If I asked you to find the zeros of x^2-3x you would first want to factor it down to x(x-3).  It becomes apparent through this equivalent but factored form that the zeros of this particular expressin are 0 and 3.  If you see when you plug in 0 you obtain 0(0-3) or 0(-3) and 0 times any number =0.  Also, when you plug in a positive 3 for x we obtain 3(3-3) or 3(0) which is also zero.

However, that is just one form of factorization.  We also have trinomials like x^2+5x+6 which will factor out to (x+3)(x+2).  Some trinomials will not have factors that turn out this nice, and you will learn the quadratic formula which will help you factor out more complicated trinomials.

Answer 4

6m - 2

The common factor between 6m and -2 is 2, therefore, you bring a number 2 out and divide 6m and -2 by 2, giving you: 2(3m - 1)