Took a quick look at this using your prompt with ChatGPT 4o this was generated.
Sure, I can help you create a worksheet based on Algebra 2 Remainder Theorem problems. Here's a set of sample problems and instructions for the worksheet:
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### Algebra 2: Remainder Theorem Worksheet
**Instructions:** For each polynomial \( P(x) \) and given divisor \( x - c \), use the Remainder Theorem to find the remainder when \( P(x) \) is divided by \( x - c \). The Remainder Theorem states that the remainder of the division of a polynomial \( P(x) \) by a linear divisor \( x - c \) is \( P(c) \).
#### Problem 1
Given \( P(x) = 3x^3 - 2x^2 + 5x - 7 \) and \( x - 2 \), find the remainder.
#### Problem 2
Given \( P(x) = 4x^4 - 5x^3 + 2x^2 - x + 1 \) and \( x + 1 \), find the remainder.
#### Problem 3
Given \( P(x) = 2x^5 - 3x^4 + 6x^3 - x^2 + 4x - 5 \) and \( x - 3 \), find the remainder.
#### Problem 4
Given \( P(x) = 5x^2 - 3x + 9 \) and \( x - 4 \), find the remainder.
#### Problem 5
Given \( P(x) = x^4 - 6x^3 + 11x^2 - 6x + 8 \) and \( x - 1 \), find the remainder.
#### Problem 6
Given \( P(x) = 7x^3 - 4x^2 + 2x - 8 \) and \( x + 2 \), find the remainder.
#### Problem 7
Given \( P(x) = x^5 - x^4 + 2x^3 - 2x^2 + x - 1 \) and \( x - 0 \), find the remainder.
#### Problem 8
Given \( P(x) = 3x^4 - 2x^3 + x^2 - 5x + 3 \) and \( x - (-3) \), find the remainder.
#### Problem 9
Given \( P(x) = 2x^3 + 5x^2 - 4x + 6 \) and \( x - 5 \), find the remainder.
#### Problem 10
Given \( P(x) = x^4 + 2x^3 - x^2 - 2x + 3 \) and \( x + 1 \), find the remainder.
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**Note:** To find the remainder using the Remainder Theorem, simply substitute the value \( c \) from the divisor \( x - c \) into the polynomial \( P(x) \).
---
Would you like this worksheet in a specific format, such as a Word document or PDF, or would you like to make any adjustments?
However
Using Google Chrome, right click on a line with a math expression and select Inspect, e.g.
and you will see HTML looking something like
Notice the lines with
- “katex-mathml”
- “katex-html”
So what is being created is not LaTeX but katex.
Since it seems you want to create a PDF and generate it from LaTeX I modified the prompt to
Create a worksheet based upon algebra 2 remainder theorem problems. Generate the output as LaTeX for use with PdfLaTeX.
which created
\documentclass[12pt]{article}
\usepackage{amsmath}
\title{Algebra 2: Remainder Theorem Worksheet}
\author{}
\date{}
\begin{document}
\maketitle
\section*{Instructions}
For each polynomial \( P(x) \) and given divisor \( x - c \), use the Remainder Theorem to find the remainder when \( P(x) \) is divided by \( x - c \). The Remainder Theorem states that the remainder of the division of a polynomial \( P(x) \) by a linear divisor \( x - c \) is \( P(c) \).
\section*{Problems}
\begin{enumerate}
\item Given \( P(x) = 3x^3 - 2x^2 + 5x - 7 \) and \( x - 2 \), find the remainder.
\item Given \( P(x) = 4x^4 - 5x^3 + 2x^2 - x + 1 \) and \( x + 1 \), find the remainder.
\item Given \( P(x) = 2x^5 - 3x^4 + 6x^3 - x^2 + 4x - 5 \) and \( x - 3 \), find the remainder.
\item Given \( P(x) = 5x^2 - 3x + 9 \) and \( x - 4 \), find the remainder.
\item Given \( P(x) = x^4 - 6x^3 + 11x^2 - 6x + 8 \) and \( x - 1 \), find the remainder.
\item Given \( P(x) = 7x^3 - 4x^2 + 2x - 8 \) and \( x + 2 \), find the remainder.
\item Given \( P(x) = x^5 - x^4 + 2x^3 - 2x^2 + x - 1 \) and \( x - 0 \), find the remainder.
\item Given \( P(x) = 3x^4 - 2x^3 + x^2 - 5x + 3 \) and \( x - (-3) \), find the remainder.
\item Given \( P(x) = 2x^3 + 5x^2 - 4x + 6 \) and \( x - 5 \), find the remainder.
\item Given \( P(x) = x^4 + 2x^3 - x^2 - 2x + 3 \) and \( x + 1 \), find the remainder.
\end{enumerate}
\end{document}
Pasting that into an online site that can convert the LaTeX to a PDF for viewing, e.g.
https://texviewer.herokuapp.com/
and clicking
This is what is displayed in the right hand panel
Notice also in the upper right the download button
which can save the file as a PDF to your local machine
On Windows I get a file dialog with this for the specific file
notice the file type is PDF. 
While I am sure you still have questions on why Katex and not Latex and exactly how to do this, which I will gladly answer, hopefully this gives you enough to see that your endeavor is worth pursuing and I would wager being accomplished successfully.
