# How do you write a polynomial with zeros -5, 2, -2 and leading coefficient 1?

Dec 28, 2016

If $a$ is a zero of a polynomial, then it can be divided by $\left(x - a\right)$.
Using this law we can write the polynomial as a product of $x - {a}_{i}$ for all zeros:
$W \left(x\right) = \left(x - \left(- 5\right)\right) \times \left(x - 2\right) \times \left(x - \left(- 2\right)\right) =$
$\left(x + 5\right) \times \left(x - 2\right) \times \left(x + 2\right) =$
$\left(x + 5\right) \times \left({x}^{2} - 4\right) = {x}^{3} + 5 {x}^{2} - 4 x + 20$