Select the correct answer from each drop-down menu. consider the following polynomials equations. 3x^2(x-1) and -3x^3+ 4x^2-2x+1 perform each operation and determine if the result is a polynomial. is the result of a + b a polynomial? yes or no is the result of a - b a polynomial? yes or no is the result of a · b a polynomial? yes or no

Yes to all 3 questions.

Step-by-step explanation:

3x^2(x-1)  +  -3x^3+ 4x^2-2x+1

= 3x^3 - 3x^2  - 3x^3 + 4x^2 - 2x + 1

=  x^2 - 2x + 1,

So A + B is a polynomial.

3x^2(x-1)  -  (-3x^3+ 4x^2-2x+1)

= 3x^3 - 3x^2 + 3x^3 - 4x^2 + 2x - 1

= 6x^3 - 7x^2 + 2x - 1.

So A - B is also a polynomial.

3x^2(x-1)( -3x^3+ 4x^2-2x+1)

= (3x^3 - 3x^2) ( -3x^3 + 4x^2 - 2x + 1)

= -9x^6 + 12x^5 - 6x^4 + 3x^3  + 9x^5 - 12x^4 + 6x^3 - 3x^2

= -9x^6 + 21x^5 - 18x^4 + 9x^3 - 3x^2.

So A * B is a polynomial.

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