Question

What is the greatest common factor of the polynomial:14z^4+10z^3+4z^2

Answer 1

Hello! First, let's write the polynomial:

`14z^4+10z^3+4z^2`

Now, let's analyze it. Look that all three coefficients are multiples of 2, and in all of them we have the unknown Z. Knowing this, we can start dividing all the polynomial by 2z, let's try it:

`(14z^4+10z^3+4z^2)/(2z)=7z^3+5z^2+2z`

Now we can do another division because we still have Z in all terms:

`(7z^3+5z^2+2z)/(z)=7z^2+5z+2`

Now we factored as much as possible, let's see:

we did two divisions, first by 2z and then by z. So, 2z * z = 2z²

According to these steps, the greatest common factor of this polynomial will be 2z², because 2z² * (7z²+5z+2) = 14z^4+10z³+4z²

Right answer: 2z²