Question

What is the greatest common factor of 5x^6+35x^4+15x^3

Answer 1

5 will go into everything. That is one of the factors.

x^3 is in everything as well.

The highest common factor is 5x^3

`(5x^6)/(5x^3) = x^(6-3) = x^3`

`(35x^4)/(5x^3) = 7x^(4-3) = 7x`

`(15x^3)/(5x^3) = 3*x^(3-3) = 3*1 = 3`

So the greatest common factor (determined by the last term) is 5x^3

And the left over polynomial is x^3 + 7x + 3