Question

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

Answer 1

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