Question

Profit, P(x), is the difference between revenue, R(2), and cost, C(2), so P(x) = R(x) - C(x) whichexpression represents P(x), if R(x) = 2x4 - 3x + 2x – 1 and C(x) = x4 – x2 + 2x + 3?

Answer 1

Given:

`\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}`

Substitute the expression of R(x) and C(x) in the expression of P(x).

`\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*1+x*-3+x^2-4 \\ P(x)=x^4-3x+x^2-4 \\ P(x)=x^4+x^2-3x-4 \end{gathered}`

Thus, the above expression of P(x) represents the simplest expression of P(x).