Adding and Subtracting Polynomials

Question 80550 • Common Core Algebra I B-IC

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?

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.

Explanation

When adding the polynomials, the leading terms combine to give x⁷ + x⁷ = 2x⁷, so the sum has degree 7. When subtracting, the x⁷ terms cancel: (x⁷ + 3x⁵ + 3x + 1) − (x⁷ + 5x + 10) = 3x⁵ − 2x − 9, which has degree 5. Therefore, the sum has degree 7 and the difference has degree 5, as choice D states.

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