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 polynomialB. 3x2 − 2x + 5; may or may not be a polynomialC. 3x2 + 8x + 3; will be a polynomialD. 3x2 + 8x + 3; may or may not be a polynomial

Answer:3x² - 2x + 5 ; will be a polynomial ⇒ answer AStep-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