Please write the functions in Python and also include explanation for each line of code and a snapshot of the code to allow for viewing of correct indentation, thank you.

Question 1 a):

Design a class named Polynomial to represent a polynomial object that contains 3 terms - The Polynomial class should contain a list of coefficients as a private data field where coefficients[0] represents a_o, coefficients[1] represents a₁ and coefficients[2] represents a₂. - Implement the __init__() method for the Polynomial class. The initializer method takes three integers, starting with a_o, to create a polynomial object. The default value for each coefficient is 1.

Test	Result
p1 = Polynomial(1, 2, 3) p2 = Polynomial(1, 2, 3) print(p1 is p2)	False

Question 1 b):

Add the __str__(self) method to the Polynomial class - The __str__(self) method is called automatically by Python whenever a Polynomial object is provided as input to the print() function. The function should return a string that represents the Polynomial object. The string returned by this method should use the ^ character to indicate exponentiation.

• If the exponent is 0, then 'x' is not printed (i.e., 2 rather than 2x^0)
• If the exponent is 1, then the exponent is not printed (i.e., 2x rather than 2x^1)
• Only terms with non-zero coefficients should be displayed
• If the coefficient of a term is 1, then the coefficient should be shown (i.e.1x + 2)
• If the coefficient of a term is negative, then a plus and a minus sign (i.e. x^2 + -2x + 2) should be shown.
• There should be a single space character on either side of a + sign that appears internal to the polynomial. The only exception to this rule is at the very start of the polynomial.
• The terms should appear in descending order of exponent value.

Test	Result
p1 = Polynomial() print(p1)	1x^2 + 1x + 1
p1 = Polynomial(3, 2, 0) print(p1)	2x + 3
p1 = Polynomial(0, 2, 3) print(p1)	3x^2 + 2x

Question 1 c):

Add the evaluate(self, x) method to the Polynomial class. - The evaluate method takes an integer value, x , as a parameter and evaluates the value of the polynomial using that value for x.

Test	Result
p = Polynomial(1, 2, 3) print(p) print(p.evaluate(2))	3x^2 + 2x + 1 17
p1 = Polynomial() print(p1) print(p1.evaluate(5))	1x^2 + 1x + 1 31
p1 = Polynomial(-3, 4, -2) print(p1) print(p1.evaluate(5))	-2x^2 + 4x + -3 -33