Question

How do you write a polynomial in standard form given zeros -1 (multiplicity 3), 3 (multiplicity 1)?

Answer 1

Polynomial is `x^4-6x^2-8x-3`

Explanation:

As the zeros are `-1` with multiplicity `3` and `3` with multiplicity `1`,

the polynomial is `(x+1)^3(x-3)`

= `(x^3+3x^2+3x+1)(x-3)`

= `x^4+3x^3+3x^2+x-3x^3-9x^2-9x-3`

or `x^4-6x^2-8x-3`