Question

How do you find a polynomial function of degree 4 with -2 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1?

Answer 1

`x^4+6x^3+12x^2+8x`

Explanation:

`y_a=(x+2)(x+2)(x+2) =x^3+6x^2+12x+8`
has `(-2)` as its only root (but with multiplicity of `3`)

`y_b =x`
has `(0)` as its only root (multiplicity of `1`)

`y = y_a* y_b = x^4+6x^3+12x^2+8x`
has `(-2)` as a root (multiplicity `3`) and `(0)` as a root (multiplicity (1))
and is of degree `4`