Greatest Common Divisors, Resultants, and Discriminants

You can compute the greatest common divisor of two polynomials using the function gcd. Here's an example:

You could also see that p and q have a factor in common by using the function resultant:

The resultant of two polynomials vanishes precisely when they have a factor in common. (In the example above we specified the variable with which we wanted to compute the resultant because the polynomials could have involved variables other than x.)