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

May 6, 2016

Polynomial is ${x}^{4} - 6 {x}^{2} - 8 x - 3$

Explanation:

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

the polynomial is ${\left(x + 1\right)}^{3} \left(x - 3\right)$

= $\left({x}^{3} + 3 {x}^{2} + 3 x + 1\right) \left(x - 3\right)$

= ${x}^{4} + 3 {x}^{3} + 3 {x}^{2} + x - 3 {x}^{3} - 9 {x}^{2} - 9 x - 3$

or ${x}^{4} - 6 {x}^{2} - 8 x - 3$