Factor out greatest common factor

Question

vshiroky · Answer

attachment

vshiroky · Answer

I don't understand how to do this at all

vshiroky · Answer

I don't know what that means though

jhannybean · Answer

$$2x^5-4x^2+16x^3$$What is your LCM between :

2, -4, 16   and  $x^5~,~ x^2~,~ x^3$?

vshiroky · Answer

x^2

jhannybean · Answer

and between 2, -4 and 16?

vshiroky · Answer

2

jhannybean · Answer

Alright, so you can factor out $2x^2$ from your equation.

jhannybean · Answer

What will your equation become when you factor that out?

vshiroky · Answer

2x^2(x^3-2x^2+8x)

misty1212 · Answer

that cannot be right, because each of the terms in the second part have an $x$ in them

vshiroky · Answer

I have no clue I'm so lost

jhannybean · Answer

If you're factoring out a $2x^2$ then your equation $2x^5-\color{red}{4x^2}+16x^3$ will just have a -2 left inside.

vshiroky · Answer

So I only take it from the one that has the exponent which is divisible?

jhannybean · Answer

Yeah, pretty much.

jhannybean · Answer

What I do is first I analyze the (2,-4,16) and I ask myself, are these all multiples of 2?

jhannybean · Answer

If they are then I find the factor that can divide into all 3 of those numbers eveny.

jhannybean · Answer

evenly*

Then I analyze $x^5~,~ x^2 ~,~ x^3$ and I ask myself the same thing, which factor of x can i pull out that will divide into the rest evenly?

vshiroky · Answer

Hmm ok I think I get it..

vshiroky · Answer

My thing says that is wrong

jhannybean · Answer

What is wrong? Can you write out what you inputted?

vshiroky · Answer

2x^5-4x^2+16x^3

jhannybean · Answer

That's not correct. Here, I will show you how to factor.

jhannybean · Answer

Earlier we got $2x^2$ as our lowest common multiple. We factor that our of our equation. $$2x^2(x^3-2+8x) \implies 2x^2(x^3+8x-2)$$Since we factored out a $2x^2$ if we multiply it to our first term, $x^3$ we will get our original, $2x^5$. Sae goes with the other two variables. $$(2x^3 \cdot 8x) = (2 \cdot 8)(x^{2 + 1})=16x^3$$$$2x^2(-2) = (2 \cdot (-2))x^2 = -4x^2$$

jhannybean · Answer

Hope that makes sense to you, @vshiroky :)

vshiroky · Answer

I still don't understand what my answer would be

jhannybean · Answer

Reread my last post please.

vshiroky · Answer

2x^2(x^3-2+8x)

jhannybean · Answer

There you go :)