Question:

Which polynomial function has the zeros 2,-1,0,-4.

Solution:

There are four zeros here, or 4 roots.

In other words, if we have a polynomial p(x) and we let x = one of the above root values, then p(x) will be zero.

So x = 2, x = -1, x = 0, ands x = -4 are all root values

We can rewrite the above as,

(x - 2) = 0, (x + 1) = 0, (x - 0) = 0, (x + 4) = 0

The above four terms are factors of a polynomial, and if we multiply then all together, the product will be zero and we will get the original polynomial, i.e.

(x - 2)(x + 1)(x - 0)(x + 4) = 0 (and of course (x = 0) is just x)

x(x - 2)(x + 1)(x + 4) = 0

multiplying out gives us,

x(x - 2)(x^2 + 5x + 4) = 0

x(x^3 + 3x^2 - 6x - 8) = 0

**x^4 + 3x^3 - 6x^2 - 8x = 0**