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Quick Math Question

Okay this question may seem a bit dumb, but it's quite confusing to me :D

It says in the textbook that if P(n) = n^2, then a polynomial f(n) that has one degree more than P(n) would be an^3+bn^2+cn+d

So my question is: What if the polynomial I have is n^2+n? What would one degree greater than it be? (including all the coefficients)

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hmm...interesting...for some reason, it sounds like this question is coming from induction unit (which we just finished! :D )

so...if P(n) = n^2, and P(n+1) = an^3+bn^2+cn+d

therefore, P(n^2+n) = P(n)(n+1) = (n^2)(an^3+bn^2+cn+d) = an^5+bn^4+cn^3+dn^2

if you have the answer then do tell me if this is right or wrong coz i may have violated some rules or not understood the math problem entirely :)

hope this helps!!

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If P(n) = n^2, then P(n) has degree 2. Therefore, f(n) has degree 3, just as you said. P(n) = an^3 + bn^2 + cn + d, which is a cubic (degree 3).

If your polynomial is n^2 + n, this is also a polynomial of degree 2, so a polynomial that is one degree greater than this will also be of degree three. It will be of the form an^3 + bn^2 + cn + d, just as the one above.

Hope that helps.

Okay this question may seem a bit dumb, but it's quite confusing to me :D

It says in the textbook that if P(n) = n^2, then a polynomial f(n) that has one degree more than P(n) would be an^3+bn^2+cn+d

So my question is: What if the polynomial I have is n^2+n? What would one degree greater than it be? (including all the coefficients)

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