Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6?
3x2 + x − 11 may or may not be a polynomial
3x2 + x − 11 will be a polynomial
3x2 + x − 1 will be a polynomial
3x2 + x − 1 may or may not be a polynomial

For this case we have the following polynomials:
[tex]P = 3x ^ 2 + 2x - 6 Q = x + 5[/tex]
By subtracting both polynomials we have:
[tex]P - Q = (3x ^ 2 + 2x - 6) - (x + 5) [/tex]
What we must do is subtract terms of the same degree.
We have then:
[tex]P - Q = 3x ^ 2 + (2x - x) + (-6 - 5) P - Q = 3x ^ 2 + x - 11[/tex]
Answer:
[tex]3x ^ 2 + x - 11[/tex] will be a polynomial

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Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6? 3x2 + x − 11 may or may not be a polynomial 3x2 + x − 11 will be a polynomial 3x2 + x − 1 will be a polynomial 3x2 + x − 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 x + 5 is subtracted from 3x2 + 2x − 6?
3x2 + x − 11 may or may not be a polynomial
3x2 + x − 11 will be a polynomial
3x2 + x − 1 will be a polynomial
3x2 + x − 1 may or may not be a polynomial