Answer:
P(x)= x ^4-3x^3+x^2-4
Step-by-step explanation:
Given data
R(x) = 2x ^4-3x^3+2x-1
c(x)=x^4-x^2+2x+3
We know that
P(x)=R(x)-C(x)
Hence
P(x)= 2x ^4-3x^3+2x-1-(x^4-x^2+2x+3)
open bracket
P(x)= 2x ^4-3x^3+2x-1-x^4+x^2-2x-3
Collect like terms
P(x)= 2x ^4-x^4-3x^3+x^2-2x+2x-3-1
P(x)= x ^4-3x^3+x^2-4
(a)
We are given
A worker on the production line is paid a base salary of $230.00 per week
so, base salary =230
Let's assume number pencils produced as x
plus $0.78 for each unit produced
now, we can find equation for earnings

now, we are given
her earnings of $446.84 for a week when she produced x units
so, we can set E(x)=446.84
and then we can solve for x







so, number of pencils = 278........Answer
(b)
If the worker had produced twice that number of units
so, number of pencils =2*278=556
now, we can find earnings

now, we can plug x=556

.................Answer