## Plot the graph of Polynomial degree 4 and 5 in Python

To plot the graph of polynomial degree 4 and 5 in python, first of all, you must know about the polynomial function.

So before continue with plotting the graph takes a look at what is a Polynomial function and degree of Polynomial. One more thing we introduce here is Polynomial Module then we move the Plot the graph of Polynomial degree 4 and 5 in Python.

## What is a polynomial function?

In mathematics, the polynomial is an expression consisting of variables (also called uncertainty) and multiples, which include addition, subtraction, multiplication, and the maintenance of non-negative integers.

Polynomial is found in the fields of mathematics and science. For example, they are used to construct polynomial equations that encode a wide range of problems from basic word problems to more complex problems; They are used to define polynomial functions found in settings ranging from basic chemistry and physics to economics and social sciences;

These are used almost exclusively in the numerical analysis of calculus and other works. In modern mathematics, polynomial rings and types of algebra are used to construct central concepts in algebra and algebraic geometry.

The polynomial function is a quadratic, cube, quarter, and a function. Only integer powers that are not negative of XPolynomial functions are the simplest, most important, and most commonly used mathematical functions. These functions can consist of one or more words with a total number of exponents.

### Degree of Polynomial

Polynomials are the sum (and difference) of polynomial "positions".

For expression of a polynomial term, any variable of the expression must have whole-number powers (or the "perceived" power of 1, as in X1, which is normally written as x). The plain number can also be a polynomial term.

Specifically, for an expression of a polynomial term, it must have no square root of the variable, no fractional or negative powers on the variable, and no fraction has any variable at all.

The degree of the polynomial is that the highest of its individual terms degree with non-zero coefficients. The degree of a word is the sum of the exponents of the variables appearing in it, and thus is a non-negative integer.

The polynomial function means that the quadratic, cubic, quartic, and so on, have only non-negative integer powers. We can give a general definition of the polynomial and its degree

For example,

f (x) = 4x³ - 3x² + 2

This function is called cubic polynomial because the 3-degree polynomial, 3 is the highest power of the x formula
f (x) = 4x²− 2x− 4

This is called a quadratic. This is a polynomial of 2 degrees because x has the highest energy of 2.

### Polynomial Module:

This module provides a number of objects (many functions) that can be used to deal with polynomial arrays, including a polynomial class that performs simple arithmetic operations.

Let us perform simple tasks using Python.

## Plotting the graph of Polynomial degree 4 in Python

``` Implement this equation using Python Code:

Python Code:
import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
x = sp.symbols('x')
a = 4*x**4+3*x**3+2*x**2+2*x+1y = np.linspace(0,10)
f = [4,3,2,2,1]
x = np.polyval(f,y)
plt.plot(x,y,'-o')
plt.xlabel('x values')
plt.ylabel('y values')
plt.title('graph of 4 degree polynomial')
plt.grid(True)
plt.show()

```
Output: ```
```
```
```
```
```
```
```
```
```
```
```
```
```
```
```
```

Expressions of roots and polynomials

import numpy as np
x = np.poly([-1,1,1,10])
print(x)
y = np.roots([1,-11,9,11,-10])
print(y)
Output:[  1. -11.   9.  11. -10.]
[10.+0.0000000e+00j -1.+0.0000000e+00j  1.+9.6357437e-09j
1.-9.6357437e-09j]

Plotting the graph of Polynomial degree 5 in Python Implement this equation using Python Code:

import numpy as np
import sympy as sp
import matplotlib.pyplot as plt
x = sp.symbols('x')
a = 10*x**5+8*x**4+7*x**3+4*x**2+2y = np.linspace(0,10)
f = [10,8,7,4,0,2]
x = np.polyval(f,y)
plt.plot(x,y,'-o')
plt.xlabel('x values')
plt.ylabel('y values')
plt.title('graph of 5 degree polynomial')
plt.grid(True)
plt.show()
Output: ```