Question

Write the polynomial given the roots: 2,-1, and -2

Answer 1

x^3 + x^2 - 4x - 4.

Explanation:

In factor form we have:

P(x) = (x - 2)(x + 1)(x + 2)

= (x + 1)(x - 2)(x + 2)

The last 2 factors simplify to the difference of 2 squares

= (x + 1)(x^2 - 4)

= x^3 - 4x + x^2 - 4

= x^3 + x^2 - 4x - 4.