# Python Program to Compute a Polynomial Equation given that the Coefficients of the Polynomial are stored in a List

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Given Coefficients of the polynomial and x which are stored in the list, the task is to compute the value of the polynomial equation with given x from the given Coefficients in Python.

Examples:

Example1:

Input:

given coefficient list = [7, 1, 3, 2]

Output:

The total value of the given polynomial 7 x^3 +1 x^2 +3 x +2 with the given value of x=5 is 917

Example2:

Input:

 given coefficient list = [3, 9, 1, 2]

Output:

The total value of the given polynomial 3 x^3 +9 x^2 +1 x +2 with the given value of x 6 = 980

## Program to Compute a Polynomial Equation given that the Coefficients of the Polynomial are stored in a List

There are several ways to compute the value of the polynomial equation with given x from the given Coefficients in Python some of them are:

### Method #1:Using for and while loop(User Input)

Approach:

• Import the math module.
• Take a empty list.
• Loop from 1 to 4 using for loop as there are 4 coefficients terms in the equation.
• Scan the coefficient as user input using int(input()) function.
• Add this to the list using append() function.
• Scan the value of x as user input using int(input()) function.
• To compute the value of the polynomial expression for the first three terms, use a for loop and a while loop and store it in a sum variable.
• To the total variable, add the fourth term.
• The computed value should be printed.
• Exit of program.

Below is the implementation:

import math
# Take a empty list.
coefflist = []
# Loop from 1 to 4 using for loop as there are 4 coefficients terms in the equation.
for t in range(4):
# Scan the coefficient as user input using int(input()) function.
elemen = int(input('Enter some random coefficient ='))
# Add this to the list using append() function.
coefflist.append(elemen)
# Scan the value of x as user input using int(input()) function.
x = int(input('Enter some random value of x ='))
# Taking a variable which stores totalValue and initialize it with 0
totalValue = 0
temp = 3
for k in range(0, 3):
while(temp > 0):
totalValue = totalValue+(coefflist[k]*(x**temp))
# breaking the while looop
break
temp = temp-1
# To the total variable, add the fourth term.
totalValue = totalValue+coefflist[3]
print("The total value of the given polynomial " +
str(coefflist[0])+' x^3 +'+str(coefflist[1])+' x^2 +'+str(coefflist[2])+' x +' +
str(coefflist[3]), 'with the given value of x=', x, 'is', totalValue)


Output:

Enter some random coefficient =1
Enter some random coefficient =9
Enter some random coefficient =3
Enter some random coefficient =5
Enter some random value of x =8
The total value of the given polynomial 1 x^3 +9 x^2 +3 x +5 with the given value of x= 8 is 1117

Explanation:

• The math module has been imported.
• The user must enter the polynomial coefficients, which are saved in a list.
• In addition, the user must input the value of x.
• The for loop, which is used to retrieve the coefficients in the list, changes the value of I from 0 to 2.
• The power for the value of x is determined by the value of j, which varies from 3 to 1.
• This method is used to compute the values of the first three terms.
• The final term is added to the total.
• The final calculated value is printed.

### Method #2: Using for and while loop(Static Input)

Approach:

• Import the math module.
• Take in the polynomial equation coefficients as static input in given list.
• Give the value of x as static input.
• To compute the value of the polynomial expression for the first three terms, use a for loop and a while loop and store it in a sum variable.
• To the total variable, add the fourth term.
• The computed value should be printed.
• Exit of program.

Below is the implementation:

import math
# Take in the polynomial equation coefficients as static input in given list.
coefflist = [7, 1, 3, 2]
# Give the value of x as static input.
x = 5
# Taking a variable which stores totalValue and initialize it with 0
totalValue = 0
temp = 3
for k in range(0, 3):
while(temp > 0):
totalValue = totalValue+(coefflist[k]*(x**temp))
# breaking the while looop
break
temp = temp-1
# To the total variable, add the fourth term.
totalValue = totalValue+coefflist[3]
print("The total value of the given polynomial " +
str(coefflist[0])+' x^3 +'+str(coefflist[1])+' x^2 +'+str(coefflist[2])+' x +' +
str(coefflist[3]), 'with the given value of x=', x, 'is', totalValue)


Output:

The total value of the given polynomial 7 x^3 +1 x^2 +3 x +2 with the given value of x=5 is 917

Explanation:

• The for loop, which is used to retrieve the coefficients in the list, changes the value of I from 0 to 2.
• The power for the value of x is determined by the value of j, which varies from 3 to 1.
• This method is used to compute the values of the first three terms.
• The final term is added to the total.
• The final calculated value is printed.

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