Each of the polynomial of the form $p(z)=a_0+\dots+a_{n-1}z^{n-1}+z^n$ satisfies the inequality $\sup\left\{\,|p(z)|\,\big\vert\,|z|\le 1\,\right\}\ge 1$
Is this statement true or false that we have to find. well MMP says that sup will be attained at $|z|=1$ so when $|z|=1$ we have $|p(z)|=|a_0+a_1\dots+ a_{n-1}+1|\le |a_0|+\dots+|a_{n-1}|+|1|$ I can not conclude more.plz help.