ccording 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 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 3x2−5x+4 3 x squared minus 5 x plus 4 3x(−1)+3x(3x)+x(−4)+x(x) 3 x left parenthesis negative 1 right parenthesis plus 3 x left parenthesis 3 x right parenthesis plus x left parenthesis negative 4 right parenthesis plus x left parenthesis x right parenthesis

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To use the Distributive Property on the expression \((3x - 1)(x - 4)\), we will distribute each term in the first parenthesis to each term in the second parenthesis.

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

2. Distributing \(-1\):
- \(-1 \cdot x = -x\)
- \(-1 \cdot (-4) = 4\)

Now we combine all these results:
\[
3x^2 - 12x - x + 4
\]
Combine the like terms (i.e., \(-12x - x\)):
\[
3x^2 - 13x + 4
\]

Thus, the expression \((3x - 1)(x - 4)\) can be rewritten as:
\[
3x^2 - 13x + 4
\]

Looking at the responses you've shared, it appears that none of the options exactly matches the correct result of \(3x^2 - 13x + 4\). Double-check to see if any option might have been misinterpreted or if there are additional choices.