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