Chebyshev Polynomials and Estimates on Monic Polynomials

We consider monic polynomials of degree n on the symmetric interval [-1,1]. We show that the absolute value of the monic polynomial is at least 2^(1-n). This result follows from the fact that the Chebyshev polynomials of degree n have lead coefficient of 2^(n-1) and oscillate between -1 and 1 on this interval at certain points. The difference between the monic polynomial and the normalized Chebyshev polynomial will give us a polynomial which we use in the proof. #mikethemathematician, #mikedabkowski, #profdabkowski