Answer:
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
