How to Calculate Volume of Polynomials

Calculating polynomial volume
••• calculatrice image by Noé Rouxel from

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)

    Things You'll Need

    • Paper
    • Pencil
    • Calculator (optional)


    • 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.

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