Respuesta :
The closure property under subtraction is shown when the correct
result from the subtraction of polynomials is also a polynomial.
Response:
- The option that shows that polynomials are closed under subtraction is; 3·x² - 2·x + 5 will be a polynomial.
How is the option that shows the closure property found?
The closure property under subtraction for the polynomials is condition
in which the result of the difference between two polynomials is also a
polynomial.
The given polynomials being subtracted is presented as follows;
(5·x² + 3·x + 4) - (2·x² + 5·x - 1)
Which gives;
(5·x² + 3·x + 4) - (2·x² + 5·x - 1) = 3·x² - 2·x + 5
Given that the result of the subtraction, 3·x² - 2·x + 5, is also a
polynomial, we have, that the option that shows that polynomials are
closed under subtraction is; 3·x² - 2·x + 5 will (always) be a polynomial.
Learn more about closure property here:
https://brainly.com/question/4334406
Answer:
A) 3x² - 2x + 5 ; will be a polynomial
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
Hope that help!
