5. (09-09-2022) Let p(n)=i=0daini where ad>0, be a degree- d polynomial in n, and let k be a constant. Prove the following properties. (a) If kd, then p(n)=O(nk). (b) If kd, then p(n)=(nk). (c) If k=d, then p(n)=(nk). (d) If k>d, then p(n)=o(nk). (e) If k0, be a degree- d polynomial in n, and let k be a constant. Prove the following properties. (a) If kd, then p(n)=O(nk). (b) If kd, then p(n)=(nk). (c) If k=d, then p(n)=(nk). (d) If k>d, then p(n)=o(nk). (e) If k