# How do you write a polynomial function given the real zeroes 1,-4, 5 and coefficient 1?

##### 2 Answers

The simplest such polynomial is:

#f(x) = (x-1)(x+4)(x-5) = x^3-2x^2-19x+20#

#### Explanation:

Convert the zeros into linear factors to find:

#f(x) = (x-1)(x+4)(x-5) = x^3-2x^2-19x+20#

Any polynomial in

Begin from the factored form to find the desired polynomial to be

#### Explanation:

An easy way of generating a polynomial with a given set of zeros is to begin with the factored form. A polynomial

Using this, we can construct the desired polynomial as follows:

Note that we could multiply by a constant to give