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18 January, 07:15

Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 + 3x + 4) - (2x2 + 5x - 1), are subtracted?

A. 3x2 - 2x + 5; will be a polynomial

B. 3x2 - 2x + 5; may or may not be a polynomial

C. 3x2 + 8x + 3; will be a polynomial

D. 3x2 + 8x + 3; may or may not be a polynomial

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Answers (2)
  1. 18 January, 07:43
    0
    the answer is A. just took the test.
  2. 18 January, 08:12
    0
    3x² - 2x + 5; will be a polynomial ⇒ answer A

    Step-by-step explanation:

    * Lets explain what is the polynomial

    - A polynomial is an expression containing two or more algebraic terms.

    - Polynomial is often the sum of some terms containing different powers

    of variables.

    - If you add or subtract polynomials, you get another polynomial.

    - If you multiply polynomials, you get another polynomial.

    * Lets solve the problem

    ∵ 5x² + 3x + 4 is polynomial

    ∵ 2x² + 5x - 1 is polynomial

    - When we subtract them the answer will be polynomial

    ∵ (5x² + 3x + 4) - (2x² + 5x - 1)

    - Open the second bracket by multiplying the negative sign by

    each term in the bracket

    ∵ - (2x²) = - 2x²

    ∵ - (5x) = - 5x

    ∵ - (-1) = 1

    ∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 5x² + 3x + 4 - 2x² - 5x + 1

    - Add the like terms

    ∴ (5x² - 2x²) = 3x²

    ∴ (3x - 5x) = - 2x

    ∵ (4 + 1) = 5

    ∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 3x² - 2x + 5

    ∴ 3x² - 2x + 5 is a polynomial

    ∴ (5x² + 3x + 4) - (2x² + 5x - 1) = 3x² - 2x + 5; will be a polynomial

    * The answer is A
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