```{exercise-end}

```

```{exercise-start}

:label: oop_ex2

```

In an {ref}`earlier exercise <pyess_ex2>`, you wrote a function for evaluating polynomials.

This exercise is an extension, where the task is to build a simple class called `Polynomial` for representing and manipulating polynomial functions such as

```{math}

:label: polynom

p(x) = a_0 + a_1 x + a_2 x^2 + \cdots a_N x^N = \sum_{n=0}^N a_n x^n

\qquad (x \in \mathbb{R})

```

The instance data for the class `Polynomial` will be the coefficients (in the case of {eq}`polynom`, the numbers $a_0, \ldots, a_N$).

Provide methods that

1. Evaluate the polynomial {eq}`polynom`, returning $p(x)$ for any $x$.

1. Differentiate the polynomial, replacing the original coefficients with those of its derivative $p'$.

Avoid using any `import` statements.

```{exercise-end}

```

## Solutions

```{solution-start} oop_ex1

:class: dropdown

```

```{solution-end}

```

```{exercise-start}

:label: oop_ex2

```

In an {ref}`earlier exercise <pyess_ex2>`, you wrote a function for evaluating polynomials.

This exercise is an extension, where the task is to build a simple class called `Polynomial` for representing and manipulating polynomial functions such as

```{math}

:label: polynom

p(x) = a_0 + a_1 x + a_2 x^2 + \cdots a_N x^N = \sum_{n=0}^N a_n x^n

\qquad (x \in \mathbb{R})

```

The instance data for the class `Polynomial` will be the coefficients (in the case of {eq}`polynom`, the numbers $a_0, \ldots, a_N$).

Provide methods that

1. Evaluate the polynomial {eq}`polynom`, returning $p(x)$ for any $x$.

1. Differentiate the polynomial, replacing the original coefficients with those of its derivative $p'$.

Avoid using any `import` statements.

```{exercise-end}

```

```{solution-start} oop_ex2

:class: dropdown

```