Variables:
p = uniform pants
c = baseball caps
Equations:


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Step 1.

Step 2.

Step 3.

Step 4.

Step 5.


Step 6.


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Baseball Pants = $23
Baseball Caps = $11
Since it is a polynomial
for the zero 4 you can write (x-4)
for the zero -14 you can write (x+14)
for the zero 5+8i since it is complex it will be accompanied with its conjugate 5-8i so you can write (x-(5+8i) and (x-(5-8i)) =(x^2-10x+89)
so
(x-4)(x+14)(x^2-10x+89)
expanding
x^4-67x^2+1450x-4984=0
We can use the fact that, for
,

Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)



By the ratio test, this series converges if

so the series has radius of convergence
.
What are you supposed to be graphing?