Is the sum of two polynomials of degree 5 always a polynomial of degree 5? Give an example to explain your answer

Question

Mathematics

Yair Ryan

15 December, 22:03

Is the sum of two polynomials of degree 5 always a polynomial of degree 5? Give an example to explain your answer

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Answers (1)

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Hayden Ware · Answer 1

A counter example is

f (x) = 5x^5+2x^3+3x

g (x) = - 5x^5-x^4+x^2-4

Then f (x) + g (x) = - x^4+2x^3+x^2+3x-4 which is a polynomial of degree 4.

So the answer is no. Counter-example is given above.