SOLUTION: please help find the GCF of the terms of each polynomial. Factor. upward arrow means that is an exponent. 16c^2 - 4c^3 + 12c^5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help find the GCF of the terms of each polynomial. Factor. upward arrow means that is an exponent. 16c^2 - 4c^3 + 12c^5      Log On


   

Question 170860: please help find the GCF of the terms of each polynomial. Factor. upward arrow means that is an exponent.
16c^2 - 4c^3 + 12c^5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how EVERY term has the variable "c" in it. So the GCF will have "c" in it. Since the smallest exponent of "c" is 2, this tells us that the exponent of "c" in the GCF will also be 2. So the variable part of the GCF is c%5E2


Now we need to find the GCF of the coefficients 16, -4, and 12. To make things simple, I'm going to make -4 positive by removing the sign (this won't change the answer).


So we need to find the GCF of 16, 4, and 12

-------------------------------------------------------

First, let's find the prime factorization of each term:


16: 2%2A2%2A2%2A2


4: 2%2A2


12: 2%2A2%2A3


Now highlight the common terms:


16: highlight%282%29%2Ahighlight%282%29%2A2%2A2


4: highlight%282%29%2Ahighlight%282%29


12: highlight%282%29%2Ahighlight%282%29%2A3


So the common terms are 2 and 2


Now simply multiply all of the common terms together to get 2%2A2=4


So the GCF of 16, 4, and 12 is 4.

----------------------------------------------------------


So this means that the GCF of 16c%5E2+-+4c%5E3+%2B+12c%5E5 is 4c%5E2


Note: this means that we can factor out the GCF from 16c%5E2+-+4c%5E3+%2B+12c%5E5 to get 4c%5E2%284+-+c+%2B+3c%5E3%29