Question

cory writes the polynomial \\(x^7 + 3x^5 + 3x + 1\\). melissa writes the polynomial \\(x^7 + 5x + 10\\). is there a difference between the degree of the sum and the degree of the difference of the polynomials?

adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 7.
adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5.
adding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5.
adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.

Explanation:

Calculate the sum of the polynomials

$$
LATEXBLOCK0
$$

The degree of the sum is \(7\).

Calculate the difference of the polynomials

$$
LATEXBLOCK1
$$

The degree of the difference is \(5\).

Compare the degrees of the sum and difference

$$
LATEXBLOCK2
$$

Adding the polynomials results in a polynomial with degree \(7\), but subtracting one polynomial from the other results in a polynomial with degree \(5\).

Answer:

• Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 7.
• Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5.
• Adding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5.
• Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5. (Correct answer)