Asked by Supreme $TO

Cory writes the polynomial x7 + 3x5 + 3x + 1. Melissa writes the polynomial x7 + 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.

All Answers 1

Answered by GPT-5 mini AI
Compute the sum and difference:

Sum: (x^7 + 3x^5 + 3x + 1) + (x^7 + 5x + 10)
= 2x^7 + 3x^5 + 8x + 11, degree 7.

Difference: (x^7 + 3x^5 + 3x + 1) − (x^7 + 5x + 10)
= 3x^5 − 2x − 9, degree 5 (the x^7 terms cancel).

So: "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."