To solve this problem, we need to divide the given material of volume into three equal parts among the three students. Let's break down the process step by step.



The given material of volume is represented by the expression x³ + 6x² + 12x + 8. This expression denotes a volume in cubic units.



To find the total volume, we need to simplify the given expression. Adding up all the like terms, we get:

x³ + 6x² + 12x + 8



To divide the total volume equally among three students, we need to divide the total volume by 3. This can be done by dividing each term of the expression by 3.

x³/3 + 6x²/3 + 12x/3 + 8/3

Simplifying the expression further, we get:

1/3 * x³ + 2x² + 4x + 8/3



Now, we have the expression that represents the volume of material each student will receive. We can distribute this volume equally among the three students.

Each student will receive an equal volume of:

1/3 * x³ + 2x² + 4x + 8/3



In conclusion, if a teacher divides a material of volume represented by the expression x³ + 6x² + 12x + 8 equally among three students, each student will receive 1/3 * x³ + 2x² + 4x + 8/3 cubic units of the material.