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Is the sum of two polynomials of degree 5 always a polynomial of degree 5

User Tyrique
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2 Answers

7 votes
No.

Example

P(x)=x^5+x+3\\ R(x)=-x^5+3x-4\\\\ P(x)+R(x)=x^5+x+3+(-x^5)+3x-4=4x-1
User Minovsky
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5 votes
The 5th degrees could cancel out to be a polynomial of degree 4. Similarly for lower degrees.
But it can't be a 6th degree.
User Closet
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8.1k points

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