For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. If there is no mistake, explain the general process for working the problem. Completely factor the polynomial: 8x^3 - 6x^2 - 2x. (1) 8x^3 - 6x^2 - 2x (2) = 2x(4x^2 - 3x - 1) (3) = 2x(4x + 1)(x - 1)

For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. If there is no mistake, explain the general process for working the problem. Completely factor the polynomial: 8x^3 - 6x^2 - 2x. (1) 8x^3 - 6x^2 - 2x (2) = 2x(4x^2 - 3x - 1) (3) = 2x(4x + 1)(x - 1)

Answer

There is no mistake in the provided solution. The process followed is correct and mathematically sound. Step-by-step explanation: 1) Identification (Line 1): Start with the expression 8x^3 - 6x^2 - 2x. 2) Factoring the Greatest Common Factor (GCF) (Line 2): Every term in the expression is divisible by 2x. Dividing each term by 2x gives: 8x^3 / 2x = 4x^2; -6x^2 / 2x = -3x; -2x / 2x = -1. This results in the factored form: 2x(4x^2 - 3x - 1). 3) Factoring the Trinomial (Line 3): Now factor the quadratic expression inside the parentheses, (4x^2 - 3x - 1). We look for two numbers that multiply to ac (4 * -1 = -4) and add to b (-3). These numbers are -4 and 1. Rewriting the middle term and grouping: 4x^2 - 4x + x - 1 = 4x(x - 1) + 1(x - 1) = (4x + 1)(x - 1). 4) Final Answer: Combining the GCF and the factored trinomial results in the final completely factored form: 2x(4x + 1)(x - 1).