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
