Chapter 11.2, Problem 25ES

Suppose $P\left(n\right)=a_m{n}^m+a_{m-1}{n}^{m-1}+\cdots +a_2{n}^2+a_{1}n+a_0$ , where all the coefficients

where all the coefficients $a_0,\text{}{a}_1,\dots ,a_m$ , are real numbers and $a_m>0$ .
a. Prove that $P\left(n\right)$is $\Omega \left(n^m\right)$by using the general procedure described in Example 11.2.4.
b. Prove that $P\left(n\right)$is $O\left(n^m\right)$ .
c. Justify the conclusion that $P\left(n\right)$is $\Theta \left(n^m\right)$