Posted November 20, 2007 Okay this question may seem a bit dumb, but it's quite confusing to me 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+dSo 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) Share this post Link to post Share on other sites

Posted November 20, 2007 hmm...interesting...for some reason, it sounds like this question is coming from induction unit (which we just finished! )so...if P(n) = n^2, and P(n+1) = an^3+bn^2+cn+dtherefore, P(n^2+n) = P(n)(n+1) = (n^2)(an^3+bn^2+cn+d) = an^5+bn^4+cn^3+dn^2if 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!! Share this post Link to post Share on other sites

Posted November 20, 2007 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 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+dSo 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) Share this post Link to post Share on other sites