Consider the followin polynomials equations a=3x2(x-1) b= -3x3+4x2-2x+1 . perform each operation and determine if the result is a polynomial. is the result of a+b a polynomial? is the result of a-b a polynomial? is the result of a*b a polynomial?

All three operations lead to polynomials.

See explanations below.

Step-by-step explanation:

Polynomial a =

Polynomial b =

Therefore:

a + b =

where we have combined all like terms. This is clearly another polynomial (of grade 2)

a - b (here we need to flip all signs inside the parenthesis when we remove this grouping symbol):

which is clearly another polynomial (but of grade 3)

a * b : (here we use distributive property to multiply each term of the first polynomial by each term of the second one, and then combine like terms)

which is indeed another polynomial (this time of grade 6)