Given:
[tex]\begin{gathered} P(x)=R(x)-C(x) \\ R(x)=2x^4-3x+2x-1 \\ C(x)=x^4-x^2+2x+3 \end{gathered}[/tex]Substitute the expression of R(x) and C(x) in the expression of P(x).
[tex]\begin{gathered} P(x)=2x^4-3x+2x-1-(x^4-x^2+2x+3) \\ P(x)=2x^4-3x+2x-1-x^4+x^2-2x-3 \\ P(x)=(2x^4-x^4)+(-3x+2x-2x)+(x^2)-3-1 \\ P(x)=x^4(2-1)+x(-3+2-2)+x^2-4 \\ P(x)=x^4\times1+x\times-3+x^2-4 \\ P(x)=x^4-3x+x^2-4 \\ P(x)=x^4+x^2-3x-4 \end{gathered}[/tex]Thus, the above expression of P(x) represents the simplest expression of P(x).
