Question

What is 2x^2 + 6x^2 + 18x factored completely?

I just want an answer. I just created a random problem, and the calculator gave a different answer than my work did, I'm wondering if I did anything wrong. Please help.

Answer 1

@mathstudent55 Wow, how'd you get to this question so fast?

Answer 2

First, factor out the common factor.
What is the GCF of the three terms?

Answer 3

2x

Answer 4

I just saw it there.

Answer 5

Oh lol

Answer 6

The GCF is 2x

Answer 7

Good.
Factor out 2x from all terms.
What do you get?

Answer 8

2x(x + 3x + 9x)

Answer 9

BTW, make the first term 2x^3, not 2x^2.

Answer 10

Don't you just add like terms and get 2x(13x)?

Answer 11

Why should I make it 2x^3?

Answer 12

Start with:
\(2x^3 + 6x^2 + 18x\)

Answer 13

The calculators all say the answer is 2x(4x+9).

Answer 14

But sure, why not. I'll change it to 2x3. Hold on, I'm editing my word docuement.

Answer 15

I tell you what. Let's do your problem first as you wrote it.
Then we'll do it with 2x^3.

Answer 16

It's okay if you want to go to 2x^3, cause I don't want to edit my docuement again. I'll just use 2x^3

Answer 17

\(2x^2 + 6x^2 + 18x\)

Before you even factor anything out, you can combine the first two terms.

Answer 18

But would that be the same if it was 2x^3?

Answer 19

Like would 2x^3 and 6x^2 be like terms?

Answer 20

Actually, can we just solve it as it is when it is 2x^3? I'm under some time pressure right now.

Answer 21

\(2x^2 + 6x^2 + 18x\)

\(= 8x^2 + 18x\)

\(= 2x(x + 9)\)

If you have the original problem, with 2x^2, this is all you can do.

Answer 22

Now let's do it with 2x^3.

Answer 23

\(2x^3 + 6x^2 + 18x\)

We start by factoring out the GCF, 2x:

\(2x(x^2 + 3x + 9)\)

This all the factoring you can do.
x^2 + 3x + 9 is not factorable.

Answer 24

Hooray for short problems!

Answer 25

LOL

Answer 26

Here's a slightly modified problem with 2x^3 and 12x^2 instead of 6x^2:

\(2x^3 + 12x^2 + 18x\)

Answer 27

@mathstudent55 Alright, so just to clarify, the only difference between factoring a polynomial with the same GCF in all the terms and factoring a polynomial that doesn't have the same GCF in all the terms is that if the GCF is the same, you have to factor it out first. After you have factored out the GCF, then you would factor as usual, correct?

Answer 28

Correct.

Answer 29

@mathstudent55 Alright, thanks for all your help on this problem as well!

Answer 30

\(2x^3 + 12x^2 + 18x\)

Factor out the GCF:

\(=2x(x^2 + 6x + 9)\)

Now we factor the trinomial:

\(=2x(x + 3)(x + 3)\)

\(= 2x(x + 3)^2\)

Answer 31

Oh, @mathstudent55 I have like 4 more questions, do you mind helping me on them?