According to the Distributive Property, which is a way to rewrite the algebraic expression (3x — 1) (x — 4)? (1 point) - - 3x2+6x+4 3x2-5x+4 3x(-1)+3x(3x) + x(−4) +x(x) 3x(x)+3x(−4) + −1(x) + −1(−4)

Answer 1

To rewrite the algebraic expression \((3x - 1)(x - 4)\) using the Distributive Property, we distribute each term in the first parenthesis by each term in the second parenthesis:

1. \(3x \cdot x = 3x^2\)
2. \(3x \cdot (-4) = -12x\)
3. \(-1 \cdot x = -x\)
4. \(-1 \cdot (-4) = 4\)

Now, we can combine these results:

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

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

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

Therefore, the rewritten expression using the Distributive Property is:

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

Among the given options, the closest match that correctly applies the Distributive Property is:

3x(x) + 3x(-4) + -1(x) + -1(-4)

This option clearly reflects the distribution process leading to the accurate expanded form of the expression.