# Find a polynomial of degree n that has only the given zero(s).

We will use the concept of factors of the polynomial to find the polynomial.

## Answer: The standard polynomial will be (x - a1) (x - a2) (x - a3).......(x - an) with a1, a2_{ },...an as their zeroes.

Let's see how we will use the concept of factors of the polynomial to find the polynomial.

**Explanation:**

When any polynomial is factorized, then the polynomial is segmented into its factors. When the factors are multiplied among themselves, then we get parent polynomial.

Let's consider that a polynomial is given whose roots/zeros are a1, a2_{, }a3 ...... an.

Then the polynomial will be equal to (x - a1) (x - a2) (x - a3).......(x - an) --(1)

We can understand better by taking a random example.

Let us consider a polynomial of degree 3 with -4, 3, and -5 as their zeroes.

so we can write x = - 4 , x = 3, x = -5

Therefore, the required polynomial will be (x + 4) (x - 3) (x + 5) [ From equation (1) ]