Question

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

Answer 1

See a solution process below:

Explanation:

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`