Mathematics

Problem

A quartic polynomial is given by

P(x)=x^{4}+px^{3}+qx^{2}+rx+s,

where

p,q,r,s\in\mathbb{R}

. The following information is known:

P(1)=0,\; P(-1)=0,\; P(2)=3

and

P(-3)=-5

. a. (i) Form four separate equations in

p, q, r, s

using the above conditions. b. (ii) Solve the system to find the values of

p, q, r,

and

s

. c. (iii) Hence write the complete polynomial

P(x)