How to Calculate Volume of Polynomials

By David Godfrey ; Updated April 24, 2017
Calculating polynomial volume

Calculating the volume of polynomials involves the standard equation for solving volumes, and basic algebraic arithmetic involving the first outer inner last (FOIL) method.

Write down the basic volume formula, which is volume=length_width_height.

Plug the polynomials into the volume formula.

Example: (3x+2)(x+3)(3x^2-2)

Utilize the first outer inner last (FOIL) method to multiply the first two equations. Further explanation of the FOIL method is found in the references section.

Example: (3x+2)*(x+3) Becomes: (3x^2+11x+6)

Multiply the last given equation (which you did not foil), by the new equation attained by foiling. Further explanation of basic polynomial multiplication is found in the references section.

Example: (3x^2-2)*(3x^2+11x+6) Becomes: (9x^4+33x^3+18x^2-6x^2-22x-12)

Combine the like terms. The result is the volume of the polynomials.

Example: (9x^4+33x^3+18x^2-6x^2-22x-12) Becomes: Volume= (9x^4+33x^3+12x^2-22x-12)


Utilize a calculator if needed when dealing with large numbers to ensure accuracy. Remember to check the signs of the numbers you are multiplying, because a negative number must be distributed throughout the polynomial.

About the Author

David Godfrey is a technology writer whose work has been featured on such sites as and LiveJournal. He has produced many articles specializing in electronics, computers and mathematics. Godfrey is a student at Florida State University pursuing a bachelor's degree in creative writing.