Which of the following shows that polynomials are closed under subtraction when polynomial 3x2 + 4 is subtracted from x2+ 2x + 5?
−2x2 + 2x + 1 may or may not be a polynomial
2x2 − 2x − 1 will be a polynomial
−2x2 + 2x + 1 will be a polynomial
2x2 − 2x − 1 may or may not be a polynomial

For this case we have the following polynomials:
[tex]3x ^ 2 + 4 x ^ 2 + 2x + 5[/tex]
Subtracting both polynomials we have:
[tex](3x ^ 2 + 4) - (x ^ 2 + 2x + 5) [/tex]
Subtracting terms from the same exponent we have:
[tex]x ^ 2 (3-1) - 2x + (4-5) [/tex]
Rewriting we have:
[tex]2x ^ 2 - 2x - 1 [/tex]
Answer:
[tex]2x ^ 2 - 2x - 1[/tex] will be a polynomial

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Which of the following shows that polynomials are closed under subtraction when polynomial 3x2 + 4 is subtracted from x2+ 2x + 5? −2x2 + 2x + 1 may or may not be a polynomial 2x2 − 2x − 1 will be a polynomial −2x2 + 2x + 1 will be a polynomial 2x2 − 2x − 1 may or may not be a polynomial

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Which of the following shows that polynomials are closed under subtraction when polynomial 3x2 + 4 is subtracted from x2+ 2x + 5?
−2x2 + 2x + 1 may or may not be a polynomial
2x2 − 2x − 1 will be a polynomial
−2x2 + 2x + 1 will be a polynomial
2x2 − 2x − 1 may or may not be a polynomial