# How do you write a polynomial with zeros 1,-4, 5?

Feb 22, 2016

Polynomial is $\left(x - 1\right) \left(x + 4\right) \left(x - 5\right)$
or ${x}^{3} - 2 {x}^{2} - 19 x + 20$

#### Explanation:

A polynomial (say with $x$ as variable) with zeros 1,-4, 5, means that when $x$ is put equal to either $1$ , $- 4$ or $5$, its value reduces to zero.

Hence the polynomial would be $\left(x - 1\right) \left(x + 4\right) \left(x - 5\right)$

or $\left(x - 1\right) \left({x}^{2} + 4 x - 5 x - 20\right)$ (multiplying last two factors)

or $\left(x - 1\right) \left({x}^{2} - x - 20\right)$

or ${x}^{3} - {x}^{2} - 20 x - {x}^{2} + x + 20$ or

${x}^{3} - 2 {x}^{2} - 19 x + 20$