To solve for the given table, let's construct it step-by-step.
1. Understanding the Structure:
- The table has 3 rows and 6 columns.
- We need to determine what values to place in each cell.
2. Filling Out the First Row:
- The first row consists of 6 columns, where the first two columns contain the variable [tex]\( x \)[/tex].
- The remaining 4 cells in this row are left blank.
- The first row is: [tex]\[ [x, x, '', '', '', ''] \][/tex]
3. Filling Out the Second Row:
- The second row is similar to the first row.
- It also has [tex]\( x \)[/tex] in the first two positions and the rest of the cells are empty.
- The second row is: [tex]\[ [x, x, '', '', '', ''] \][/tex]
4. Filling Out the Third Row:
- The third row has a different pattern. The first two cells contain [tex]\( x^2 \)[/tex].
- The remaining four cells in the third row contain the variable [tex]\( x \)[/tex].
- The third row is: [tex]\[ [x^2, x^2, x, x, x, x] \][/tex]
5. Combining All Rows:
- Combining everything, we have:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & x & & & & \\
\hline
x & x & & & & \\
\hline
x^2 & x^2 & x & x & x & x \\
\hline
\end{array}
\][/tex]
Thus, the entire table looks like:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
x & x & & & & \\
\hline
x & x & & & & \\
\hline
x^2 & x^2 & x & x & x & x \\
\hline
\end{tabular}
\][/tex]
