How do you find the GCF of #15g ^ { 6} - 20g ^ { 4} + 35g ^ { 2}#?

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Answer 1 · 2018-06-17T16:26:59

See a solution process below:

First, factor each term as:

#15g^6 = 3 * 5 * g * g * g * g * g * g#

#20g^4 = 2 * 2 * 5 * g * g * g * g#

#35g^2 = 5 * 7 * g * g#

Next, identify the common factors in each term:

#15g^6 = 3 * color(red)(5) * color(red)(g) * color(red)(g) * g * g * g * g#

#20g^4 = 2 * 2 * color(red)(5) * color(red)(g) * color(red)(g) * g * g#

#35g^2 = color(red)(5) * 7 * color(red)(g) * color(red)(g)#

Therefore, the GCF of the three terms is:

#GCF = color(red)(5) * color(red)(g) * color(red)(g) = 5g^2#