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18 December, 16:47

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

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Answers (2)
  1. 18 December, 16:54
    0
    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.
  2. 18 December, 17:01
    0
    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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