Sure, let's break down the phrase "The quotient of 3 and the cube of a number" step-by-step to form an algebraic expression:
1. Identify the number: In the problem, "a number" is represented by the variable [tex]\( x \)[/tex].
2. Cube of the number: The cube of [tex]\( x \)[/tex] is written as [tex]\( x^3 \)[/tex].
3. Quotient of 3 and the cube of a number: The word "quotient" implies a division. Therefore, we are dividing 3 by the cube of [tex]\( x \)[/tex].
Putting it all together, the algebraic expression that represents the phrase is:
[tex]\[ \frac{3}{x^3} \][/tex]
Thus, the answer is:
[tex]\[ \frac{3}{x^3} \][/tex]
