Question

What is a polynomial with a single root at x = -3 and a triple root at x = 4?

Answer 1

x = -3
x + 3 = 0. Therefore, (x+3) is a factor.

x = 4
x - 4 = 0. Therefore, (x-4) is a factor. And since it is a triple root, (x-4)^3 is a factor.

The simplest polynomial is: (x+3)(x-4)^3.
You can multiply it out if necessary.