How do you write a polynomial function of least degree with integral coefficients that has the given zeros 5/3, 1, -1?

May 24, 2017

$p \left(x\right) = 3 {x}^{3} - 5 {x}^{2} - 3 x + 5$

Explanation:

$\left(x - \frac{5}{3}\right) \left(x - 1\right) \left(x + 1\right) = 0$

$\left(3 x - 5\right) \left({x}^{2} - 1\right) = 0$

$3 {x}^{3} - 3 x - 5 {x}^{2} + 5 = 0$