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

$\dfrac{5x^6}{5x^3} = x^(6-3) = x^3$

$\dfrac{35x^4}{5x^3} = 7x^(4-3) = 7x$

$\dfrac{15x^3}{5x^3} = 3*x^(3-3) = 3*1 = 3$

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

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