polynomials.py

import marimo

__generated_with = "0.9.33"
app = marimo.App(width="medium")


@app.cell
def __():
    import marimo as mo
    return (mo,)


@app.cell
def __(mo):
    mo.md(
        r"""
        ### Rational Zeroes Theorem
        The rational zeroes theorem can be used to find _rational_ numbers than may possibly be roots of the polynomial. Methods like synthetic
        substituion can be used to find out which ones are actually roots.

        #### Example
        Consider the polynomial $6x^3+11x^2-3x-2$.  
        Find the factors of the leading coefficient ($6$ from $6x^3$) and the constant ($-2$).  
        The factors of $6$ are $\pm\{1,2,3,6\}$. The factors of $-2$ are $\pm\{1,2\}$.  
        The factors of the constant over the factors of the leading coefficient are the possible rational zeoes.  
        The possible rational zeroes of the polynomial are $\pm\{1,2,\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{1}{6}\}$.
        """
    )
    return


if __name__ == "__main__":
    app.run()