According to the Distributive Property, which is a way to rewrite the algebraic expression (3x−1)(x−4) ?(1 point) Responses 3x2+6x+4 3 x squared plus 6 x plus 4 3x2−5x+4 3 x squared minus 5 x plus 4 3x(x)+3x(−4)+−1(x)+−1(−4) 3 x left parenthesis x right parenthesis plus 3 x left parenthesis negative 4 right parenthesis plus negative 1 left parenthesis x right parenthesis plus negative 1 left parenthesis negative 4 right parenthesis 3x(−1)+3x(3x)+x(−4)+x(x)

Answer 1

To rewrite the expression \((3x−1)(x−4)\) using the Distributive Property (also known as the FOIL method for binomials), we distribute each term in the first binomial by each term in the second binomial.

Let's do the multiplication step-by-step:

1. First Terms: \(3x \cdot x = 3x^2\)
2. Outer Terms: \(3x \cdot (-4) = -12x\)
3. Inner Terms: \(-1 \cdot x = -1x\)
4. Last Terms: \(-1 \cdot (-4) = 4\)

Now, we can combine these results:

\[ 3x^2 - 12x - 1x + 4 \]

Combining \(-12x - 1x\):

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

So, the expression \((3x−1)(x−4)\) rewrites to:

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

Among the given options, none of them match this result. However, if it's assumed there was a typo in the options, it seems like the closest response is:

3x² − 5x + 4, but mathematically, the correct answer is:

3x² − 13x + 4.