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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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  1. 16 December, 00:58
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    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.
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