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

asked Feb 14, 2018 153k views

1 vote

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7 votes

No.

Example

$P(x)=x^5+x+3\\ R(x)=-x^5+3x-4\\\\ P(x)+R(x)=x^5+x+3+(-x^5)+3x-4=4x-1$

Minovsky answered Feb 16, 2018

6.2k points

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.

Closet answered Feb 18, 2018

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