# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 1, -4, 5?

$\left(x - 1\right) \left(x + 4\right) \left(x - 5\right)$
Since the zeros are at 1, -4 and 5, it follows that $x - 1$, $x + 4$ and $x - 5$. Since we are looking for the least degree polynomial, it must be $c \left(x - 1\right) \left(x + 4\right) \left(x - 5\right)$. The constant $c$ is fixed at 1 by the demand that the leading coefficient is 1.