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

Oct 15, 2016

The equation is $y = {x}^{3} - 2 {x}^{2} - 19 x + 20$

#### Explanation:

A polynomial in factored form, is written as $y = a \left(x - a\right) \left(x - b\right) \left(x - c\right) \ldots$ where $a , b , c , \ldots$ are the zeroes and $a$ is the leading coefficient.

Hence, we can write the polynomial function as

$y = 1 \left(x - 1\right) \left(x + 4\right) \left(x - 5\right)$

If you want this in standard form, simply multiply out.

$y = 1 \left({x}^{2} + 3 x - 4\right) \left(x - 5\right)$

$y = {x}^{3} + 3 {x}^{2} - 4 x - 5 {x}^{2} - 15 x + 20$

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

Hopefully this helps!