According to the Distributive Property, which is a way to rewrite the algebraic expression (3x - 1) * (x - 4)' ( 1 point) 3x(- 1) + 3x(3x) + x(- 4) + x(x); 3x ^ 2 + 6x + 4; 3x ^ 2 - 5x + 4; 3x(x) + 3x(- 4) - (x) - (- 4)

Answer 1

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, we need to apply the distributive property to each term in the first parentheses with each term in the second parentheses.

Let's multiply the terms step by step:

1. Multiply \(3x\) by \(x\):

   \[ 3x \cdot x = 3x^2 \]

2. Multiply \(3x\) by \(-4\):

   \[ 3x \cdot (-4) = -12x \]

3. Multiply \(-1\) by \(x\):

   \[ -1 \cdot x = -x \]

4. Multiply \(-1\) by \(-4\):

   \[ -1 \cdot (-4) = 4 \]

Now, combine all these results together:

\[ 3x^2 - 12x - x + 4 \]

Combine the like terms \(-12x\) and \(-x\):

\[ 3x^2 - 13x + 4 \]

However, that option isn't in your list. Based on the options you've provided, it seems there is some confusion. The closest expression from your list is:

3x² - 5x + 4.

Please double-check the options to ensure accuracy, but from my calculations, the correct expanded form is 3x² - 13x + 4.