# How do you write a polynomial in standard form given the zeros x=-6, 2, and 5?

##### 2 Answers

A polynomial with zeros

#### Explanation:

You are given the following information about the polynomial: zeros.

Definition of zeros: If x = zero value, the polynomial becomes zero. i.e. If you plug in -6, 2, or 5 to x, this polynomial you are trying to find becomes zero.

For the polynomial to become zero at let's say x = 1, the polynomial needs to contain the following term:

This looks too simple, and polynomials are usually bigger. They are usually quadratic, cubic, quartic, etc.

However, those messy polynomials all have

Because we have 3 zeros, we write the same kind of equation for each zero.

You multiply all of them to get the following equation.

If you are wondering why we multiply them, I'll give you a hint. Zero multiplied by any number is zero. So if one of the three equations above becomes zero, does it matter what values the other two equations give?

Expand the equation:

And there's your answer!

One extra note: a more complete answer would be

The polynomial equation with roots a, b and c is

#### Explanation:

The cubic equation with roots a, b and c is

Here (a, b, c) = (6, 2, 5).

a+b+c+ 13, bc+ca+ab=52 abd abc=60