How do you factor out the greatest common factor of #112x^9y^9 + 144x^5y^5+128x^7y^3#?

2 Answers
Ryoksos
Mar 22, 2017

#16x^5y^3#

Explanation:

First, you look at only the coefficients. Find all of their prime factors, in this case they are respectively: #7*2*2*2*2#, #3*3*2*2*2*2#, and #2*2*2*2*2*2*2#. Once you've done that, determine every factor that they have in common. In this case, they all have at least four two's. Once those four two's are taken out though, they have nothing else all in common so #2^4# will be our coefficient which is 16.

Now, look at the two variables. Whichever term has the lowest power of x is the power of x that you will use because the other terms have at LEAST that power of x so they have that in common. In this case it is 5. For y it is 3. So the answer is #16x^5y^3#. Hope I helped!

Barney V.
Mar 22, 2017

#16x^5y^3(7x^4y^6+9y^2+8x^2)#

Explanation:

#112x^9y^9+144x^5y^5+128x^7y^3#

#:.=16x^5y^3(7x^4y^6+9y^2+8x^2)#

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