Hey, I have a homework problem in which I have to multiply two polynomials. I am assuming that the 2 polynomials can each be of any length so I am stuck as to how I am supposed to do that. My homework sheet derives how to do it like this (not sure how to write it in text, but the variable/number after a is under it):

```
p1 = anx^n + ... + a1x + a0
p1*p2 = (anx^n + ... + a1x + a0) * p2
= (anx^n + ... + a1x) * p2 + a0 x p2
= (anx^n + ... + a1) * (p2 * x) + a0 * p2
= shiftRight(p1) * shiftLeft(p2) + constCoef(p1) * p2
(Explains that if you keep shifting right it will eventually be 0, and the answer is straight forward)
```

I also have some code already done that does the functions above. Also note that polynomials in this homework are put into lists, and reversed. Meaning that the polynomial 3x+2 = [2,3]

```
# Standardizes the polynomial (Gets rid of trailing 0s)
def standardize(lst):
if lst[len(lst)-1] == 0:
lst.pop()
return lst
# Finds if the polynomial is 0
def isZeroPoly(lst):
if lst == []:
return True
else:
return False
# Adds 2 polynomials ([2,3],[4,5] => [6,8])
def addPoly(lst1,lst2):
result = []
if len(lst1) > len(lst2):
for x in range(0,len(lst1)):
if len(lst2)-1 < x:
result.append(lst1[x])
else:
result.append(lst1[x] + lst2[x])
else:
for x in range(0,len(lst2)):
if len(lst1)-1 < x:
result.append(lst2[x])
else:
result.append(lst1[x] + lst2[x])
standardize(result)
return result
# Scales the polynomial by the scale variable ((3,[1,2,3]) => [3,6,9])
def scalePoly(scale,lst):
for x in range(0,len(lst)):
lst[x] = (lst[x] * scale)
standardize(lst)
return lst
# Gives the constant in the polynomial ([2,3,4] => [2])
def constCoef(lst):
constant = lst[0]
return constant
# Shifts the polynomial left ([2,3,4] => [0,2,3,4])
def shiftLeft(lst):
newlst = []
newlst.append(0)
for x in range(0,len(lst)):
newlst.append(lst[x])
return newlst
# Shifts the polynomial right ([2,3,4] => [3,4])
def shiftRight(lst):
lst.remove(lst[0])
return lst
def mulPoly(lst1,lst2):
result = []
result1 = []
for x in range(0,len(lst1)):
for y in range(0,len(lst2)):
result.append(lst1[x] * lst2[y])
return result
count = 0
end = result.pop()
result1 = []
result1.append(result[0])
for x in range(1,len(result),2):
result1.append(result[x] + result[x+1])
result1.append(end)
return result1
```

The mulPoly function that I came up with quickly will only work with 2 2 term polynomials which is why I need help. Specifically I'm looking for either a different method or a way to make my method able to accept different sized polynomials and larger polynomials. Thanks for any help.