Final answer:
Upon expanding the given expression (x - 2) × (3x + 1) × (4x - 3), none of the provided options a, b, c, or d is correct. The correct result of the expansion, obtained through step-by-step multiplication, is 12x³ - 29x² + 7x + 6.
Step-by-step explanation:
To calculate (x - 2) × (3x + 1) × (4x - 3) when x is a real number, we should use the distributive property of multiplication over addition, which means we will expand the expression step-by-step.
First, focus on multiplying the two binomials: (x - 2) × (3x + 1). This will give us:
- x * 3x = 3x²
- x * 1 = x
- -2 * 3x = -6x
- -2 * 1 = -2
Combining these terms gives us: 3x² + x - 6x - 2 = 3x² - 5x - 2.
Now we take 3x² - 5x - 2 and multiply it by the third binomial (4x - 3):
- 3x² * 4x = 12x³
- 3x² * (-3) = -9x²
- -5x * 4x = -20x²
- -5x * (-3) = 15x
- -2 * 4x = -8x
- -2 * (-3) = 6
Combine like terms to get the final result: 12x³ - 9x² - 20x² + 15x - 8x + 6 which simplifies to 12x³ - 29x² + 7x + 6.
Therefore, none of the options a, b, c, or d provided is the correct expansion.