Write a program to input pairs of polynomials and output: 1. Output them in canonical form.

Then compute and output:

2. Their sum (add them)

3. Their difference (subtract them) 4. Their product (multiply them).

Question: What do we mean by canonical form?

Answer: This is a representation where

(a) The polynomial is written from the highest powers to the lowest, and

(b) All terms with the same power are consolidated. If the consolidation leads to a zero coefficient, do not display that term.

Example: If the input were

-1+5x+20x^3-9x^2-2x+x^2-2x^3+x^9, You would change it to:

x^9+18x^3-8x^2+3x-1 The input:

Read the input from a file called input.txt in the same directory as your program.

Each line (terminated by a newline character) in the file will represent a polynomial. The line will contain a list of integers, which when taken in pairs, will represents the coefficient and exponent of each of the terms in the polynomial.

Processing and output:

You will process each pair of lines, representing two polynomials and will: 1. Output them first as they appear in the file and then in canonical form. Then compute and output, all in canonical form:

2. Their sum (add them)

3. Their difference (subtract them) 4. Their product (multiply them).

Output them to a file in your programs directory called output.txt