Question

According to the Distributive Property, which is a way to rewrite the algebraic expression (3x - 1) (x - 4)? (1 point)
о 3х (х) + 3x (-4) + - -1(x) + -1(-4)
• 3х (-1) + 3х (3x) + x (-4) + x(x)
О 3х2 - 5x + 4
0 3х2 + 6x + 4

Answer 1

To apply the Distributive Property to the expression \((3x - 1)(x - 4)\), we use the formula \((a + b)(c + d) = ac + ad + bc + bd\). Here, we have:

- \(a = 3x\)
- \(b = -1\)
- \(c = x\)
- \(d = -4\)

Now we can calculate:

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

Now add these results together:

\[
3x^2 - 12x - x + 4 = 3x^2 - 13x + 4
\]

None of the provided options exactly match \(3x^2 - 13x + 4\). However, if we look closely at the choices provided, it seems like there might have been a typographical error or miscalculation in the options, as the closest result (though not correct) is:

- \(3x^2 - 5x + 4\)

If you wanted the correct answer according to the Distributive Property based on calculations done, it should really be \(3x^2 - 13x + 4\).

Thus, based on the provided options, none are accurate; the correct answer is that the expression rewrites to \(3x^2 - 13x + 4\).