Make Polynomial from Zeros

This calculator create the term of the simplest polynomial from the given zeros. The simplest polynomial has a leading coefficient of 1. The leading coefficient is the number before the variable with the largest exponent. Further polynomials with the same zeros can be found by multiplying the simplest polynomial with a factor.
The polynomial can be up to fifth degree, so have five zeros at maximum. Please enter one to five zeros separated by space. More zeros are ignored.

Example: with the zeros -2 0 3 4 5, the simplest polynomial is x⁵-10x⁴+23x³+34x²-120x. Factorized it is written as (x+2)*x*(x-3)*(x-4)*(x-5).

The notation allows you to choose whether the polynomial should be easier to read or easier to copy. In the notation x^n, the polynomial e.g. can be used at the function graphs plotter.

The term polynomial means multiple-named. The individual powers of a variable are considered individual names. The degree of a polynomial corresponds to its highest exponent. Thus, in a fifth-degree polynomial, x⁵ occurs; x with lower exponents may also occur, but are not required. The exponents are always integers and greater than or equal to zero. x⁰ always equals 1 and can therefore be omitted; in this case, only the coefficient is written, since multiplying with 1 is unnecessary. The coefficient is the number in front of each x. If the xⁿ are ordered in descending order of their powers, the leading coefficient is at the first place.
Multiplying a complete polynomial by a number other than 0 does not change its zeros. Such multiplication is done by multiplying each individual coefficient by this number. If this number is greater than 1, the polynomial graph becomes steeper; between 0 and 1, it becomes flatter; and for -1, it is reflected at the x-axis. For other negative values, it becomes flatter or steeper depending on their absolute value, as with positive numbers.