Question 170860
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^2}}}



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


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



{{{16}}}: {{{2*2*2*2}}}



{{{4}}}: {{{2*2}}}



{{{12}}}: {{{2*2*3}}}



Now highlight the common terms:



{{{16}}}: {{{highlight(2)*highlight(2)*2*2}}}



{{{4}}}: {{{highlight(2)*highlight(2)}}}



{{{12}}}: {{{highlight(2)*highlight(2)*3}}}



So the common terms are 2 and 2



Now simply multiply all of the common terms together to get {{{2*2=4}}}



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


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So this means that the GCF of {{{16c^2 - 4c^3 + 12c^5}}} is {{{4c^2}}}



Note: this means that we can factor out the GCF from {{{16c^2 - 4c^3 + 12c^5}}} to get {{{4c^2(4 - c + 3c^3)}}}