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…

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asked Feb 11, 2018 119k views

2 Answers

Benjamin Thiel · Answer 1 · 2018-02-14T00:13:36+0000

Yes, there is a difference between the degree of the sum and the difference of the polynomials.

Yes, there is a difference between the degree of the sum and the degree of the difference of the polynomials.

The degree of a polynomial is determined by the highest power of x in the polynomial. For the polynomial
x^7 + 3x^5 + 3x + 1 , the degree is 7.

When adding or subtracting polynomials, we combine like terms.

In this case, the degree of the sum and the difference will be the same as the highest degree of the terms being added or subtracted.

In the given polynomials, both have a term with
x^7, so the sum and the difference will have a degree of 7.