According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4)?(1 point) Responses 3x2−5x+4 3 x squared minus 5 x plus 4 3x(−1)+3x(3x)+x(−4)

Answer 1

To rewrite the expression \((3x - 1)(x - 4)\) using the Distributive Property, you need to multiply each term in the first parentheses by each term in the second parentheses.

So:

\[ (3x - 1)(x - 4) = 3x \cdot x + 3x \cdot (-4) - 1 \cdot x - 1 \cdot (-4) \]

This simplifies to:

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

Combining like terms gives:

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

None of the given response options match the correct expanded form of the expression. Therefore, if the provided options are:

• 3x²−5x+4
• 3 x squared minus 5 x plus 4
• 3x(−1)+3x(3x)+x(−4)

None of them are correct because they do not reflect the proper expansion of \((3x - 1)(x - 4)\). The correct answer is \(3x^2 - 13x + 4\).