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

the answer is A. just took the test.

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