need help factoring the polynomials using gcf

Question

20u8k3+48u7k5-12u6k4

Answer 1

What do you think is the greatest common factor (GCF)?

It must contain factors common to ALL terms.

First, examine the coefficients. 4 goes into 20, into 48, and into 12; other factors of these numbers are, respectively, 4, 12 and 3, but there's nothing in common, so we settle for GCF's numerical component being 4.

 

Next, we must assume that you have variable factors WITH EXPONENTS, which you neglected to put "upstairs".

Anyway, surveying those three terms, the greatest COMMON exponent of u is 6, so u⁶ is a component of the GCF.

Surveying for greatest common exponent on k, we decide that k³ is also a component of the GCF.

 

GCF =4u⁶k³

expression = 4u⁶k³(5u² + 12uk² - 3k)

 

As always, check the work.