Question

Determine the GCF for each of the polynomials.

Answer 1

${2x}^{3} - {7x}^{2} + 3x \\ = x( {2x}^{2} - 7x + 3)$
GCF is x.

${33x}^{4} - 22 \\ = 11( {3x}^{4} - 2)$
GCF is 11.

${24x}^{5} - {56x}^{3} + 16x \\ = 8x( {3x}^{4} - {7x}^{2} + 2)$
GCF is 8x.

Hope this helps. - M

Answer 2

#1) The GCF is x.
#2) The GCF is 11.
#3) The GCF is 8x.

For #1, the only thing each term has in common is an x.  This makes it the GCF.
For #2, both terms are divisible by 11.  Neither of them have a variable, so the GCF does not include x.  11 is the GCF.
For #3, all of the terms are divisible by 8.  Additionally, they all have an x.  This makes the GCF 8x.