Factor completely: 18m^3 − 12m^2 + 6m

Question

anonymous · Answer

6m (3m^2 − 2m + 1)

 2m (9m^2 − 6m + 3)

 6 (3m^3 − 2m2 + m)

 6m (3m^2 − 2m)

anonymous · Answer

I know it is not B or C but do you get 1 after taking out the 6m?

mathstudent55 · Answer

What factor do all terms have in common?

anonymous · Answer

so what do $$18m ^{3}-12m ^{2}+6m$$ have in common

anonymous · Answer

6m, I solved it but when yuo factor it do you leave a 1 at the end or no?

mathstudent55 · Answer

Good. When you factor out he 6m, you will have to have three terms inside the parentheses.

mathstudent55 · Answer

Yes, you must leave the 1 at the m.

anonymous · Answer

Oh ok I see.

mathstudent55 · Answer

Remember that factoring is the opposite of multiplying out.

mathstudent55 · Answer

Look at this simple example.
Factor: 9x^2 + 3x

mathstudent55 · Answer

Here, the common factor is 3x, right?

anonymous · Answer

yupp because 9 has x^2

mathstudent55 · Answer

Right.

We factor out the 3x:
Do we get 3x(3x) or 3x(3x + 1)?

anonymous · Answer

I guess 3x + 1 because you have to leave a placeholder basically right?

mathstudent55 · Answer

All you need to do is multiply out our two possibilities. Whichever one gives you back what you started with is the correct answer.

mathstudent55 · Answer

Let's do both multiplications:

3x(3x) = 9x^2

3x(3x + 1) = 9x^2 + 3x

Since only the second choice gives us the original binomial back, the second choice is the correct factorization.

anonymous · Answer

Ah ok, so basically we leave it because 1 never really affects anyhing, like 2*1 = 2

mathstudent55 · Answer

Correct. The 1 needs to be there to have something to multiply the factored out 3x to end up with 9x^2 + 3x.

anonymous · Answer

Ah I see, interesting concept :D you taught me plenty

mathstudent55 · Answer

Right. Remember in our example, if you leave out the 1 in the factorization, you end up multiplying back together and ending up with only 9x^2, not the 9x^2 + 3x expression we started with.

anonymous · Answer

Yes because when you distribute it out in keeps 3x intact since it is only 1

mathstudent55 · Answer

Right.

What you need to remember is that factorization and multiplication are opposite operations. Factorization is undoing a multiplication. If you ever need to check if a factorization was done correctly, just multiply it out. You must end up with the original expression. If you don't the factorization is incorrect.

anonymous · Answer

Ah I see, wel thanks a bunch though really helped :)

mathstudent55 · Answer

You're welcome.

anonymous · Answer

Now I know what OpenStudy is about :D

mathstudent55 · Answer

Great. Keep asking questions.