profit, $p(x)$, is the difference between revenue, $r(x)$, and cost, $c(x)$, so $p(x)=r(x)-c(x)$. which…

profit, $p(x)$, is the difference between revenue, $r(x)$, and cost, $c(x)$, so $p(x)=r(x)-c(x)$. which expression represents $p(x)$, if $r(x)=2x^{4}-3x^{3}+2x - 1$ and $c(x)=x^{4}-x^{2}+2x + 3$?\n$x^{4}-3x^{3}-x^{2}+4x + 2$\n$2x^{8}-3x^{3}+x^{2}-4$\n$x^{4}-3x^{3}+x^{2}-4$\n$3x^{4}-3x^{3}-x^{2}+4x + 2$

profit, $p(x)$, is the difference between revenue, $r(x)$, and cost, $c(x)$, so $p(x)=r(x)-c(x)$. which expression represents $p(x)$, if $r(x)=2x^{4}-3x^{3}+2x - 1$ and $c(x)=x^{4}-x^{2}+2x + 3$?\n$x^{4}-3x^{3}-x^{2}+4x + 2$\n$2x^{8}-3x^{3}+x^{2}-4$\n$x^{4}-3x^{3}+x^{2}-4$\n$3x^{4}-3x^{3}-x^{2}+4x + 2$

Answer

Explanation:

Step1: Substitute given functions

Given $P(x)=R(x)-C(x)$, $R(x) = 2x^{4}-3x^{3}+2x - 1$ and $C(x)=x^{4}-x^{2}+2x + 3$. So $P(x)=(2x^{4}-3x^{3}+2x - 1)-(x^{4}-x^{2}+2x + 3)$.

Step2: Remove parentheses

$P(x)=2x^{4}-3x^{3}+2x - 1 - x^{4}+x^{2}-2x - 3$.

Step3: Combine like - terms

For the $x^{4}$ terms: $2x^{4}-x^{4}=x^{4}$; for the $x^{3}$ term: $-3x^{3}$ remains the same; for the $x^{2}$ term: $x^{2}$ remains the same; for the $x$ terms: $2x-2x = 0$; for the constant terms: $-1-3=-4$. So $P(x)=x^{4}-3x^{3}+x^{2}-4$.

Answer:

$x^{4}-3x^{3}+x^{2}-4$