Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive at this answer.

Answer:

To find the volume of the rectangular prism, use the formula V = lwh. 1. Substitute the given expressions into the formula: V = [(24x^2 + 6x) / (x - 1)] * (2x - 5) * [(x^2 - x) / (4x + 1)]. 2. Write 2x - 5 as a fraction over 1: (2x - 5) / 1. 3. Factor the expressions where possible: - 24x^2 + 6x factors to 6x(4x + 1). - x^2 - x factors to x(x - 1). 4. Rewrite the volume expression with factored components: V = [6x(4x + 1) / (x - 1)] * [(2x - 5) / 1] * [x(x - 1) / (4x + 1)]. 5. Divide out (cancel) the common factors found in the numerator and denominator, which are (4x + 1) and (x - 1). 6. Multiply the remaining factors: V = (6x) * (2x - 5) * (x), which simplifies to (x)(6x)(2x - 5) or 6x^2(2x - 5).