Sure, let's match each verbal description with the appropriate algebraic expression:
1. The difference of 5 times the cube of [tex]\( x \)[/tex] and the quotient of 4 times [tex]\( x \)[/tex] and 3
- Here, we are first calculating the cube of [tex]\( x \)[/tex], then multiplying it by 5, and then subtracting the result of the division of [tex]\( 4x \)[/tex] by 3 from it. The correct algebraic expression is [tex]\( 5x^3 - \frac{4x}{3} \)[/tex].
2. 5 times the cube of [tex]\( x \)[/tex] divided by 4 times [tex]\( x \)[/tex]
- This expression is straightforward, as it directly mentions multiplying [tex]\( x^3 \)[/tex] by 5 and then dividing the result by [tex]\( 4x \)[/tex]. The correct algebraic expression is [tex]\( \frac{5x^3}{4x} \)[/tex].
3. The quotient of the difference of 5 times [tex]\( x \)[/tex] cubed and 4 and [tex]\( x \)[/tex]
- First, we form the difference [tex]\( 5x^3 - 4 \)[/tex], and then we divide this difference by [tex]\( x \)[/tex]. The correct algebraic expression is [tex]\( \frac{5x^3 - 4}{x} \)[/tex].
4. The cube of the difference of 5 times [tex]\( x \)[/tex] and 4
- Here, we first form the difference [tex]\( 5x - 4 \)[/tex], and then we take the cube of this difference. The correct algebraic expression is [tex]\( (5x - 4)^3 \)[/tex].
Now let's place these expressions in the table next to the corresponding descriptions:
\begin{tabular}{|l|l|}
\hline
\begin{tabular}{l}
the difference of 5 times the cube of [tex]$x$[/tex] cubed and \\
the quotient of 4 times [tex]$x$[/tex] and 3
\end{tabular} &
[tex]$5 x^3-\frac{4 x}{3}$[/tex] \\
\hline
5 times the cube of [tex]$x$[/tex] divided by 4 times [tex]$x$[/tex] &
[tex]$\frac{5 x^3}{4 x}$[/tex] \\
\hline
the quotient of the difference of 5 times [tex]$x$[/tex] cubed and 4 and [tex]$x$[/tex] &
[tex]$\frac{5 x^3-4}{x}$[/tex] \\
\hline
the cube of the difference of 5 times [tex]$x$[/tex] and 4 &
[tex]$(5 x-4)^3$[/tex] \\
\hline
\end{tabular}
This completes the matching of each verbal description with the corresponding algebraic expression.
