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.

Answer: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.