Question

When simplified, which expressions produce the trinomial 4x^2 - 20x - 24? Select the two that apply. ( 2 points)
−4(x^2+5x+6)
4(x^2−20x−24)***********
4(x−6)(x+1)
4(x^2−5x−6)***********

Answer 1

To determine which given expressions simplify to the trinomial \( 4x^2 - 20x - 24 \), we'll simplify each expression one by one.

1. **Expression: \( -4(x^2 + 5x + 6) \)**

\[
-4(x^2 + 5x + 6) = -4x^2 - 20x - 24
\]

This simplifies to \( -4x^2 - 20x - 24 \), which does not match \( 4x^2 - 20x - 24 \).

2. **Expression: \( 4(x^2 - 20x - 24) \)**

\[
4(x^2 - 20x - 24) = 4x^2 - 80x - 96
\]

This simplifies to \( 4x^2 - 80x - 96 \), which does not match.

3. **Expression: \( 4(x - 6)(x + 1) \)**

First, we expand \( (x - 6)(x + 1) \):
\[
(x - 6)(x + 1) = x^2 - 6x + x - 6 = x^2 - 5x - 6
\]
Now multiplying by 4:
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]

This simplifies to \( 4x^2 - 20x - 24 \), which matches.

4. **Expression: \( 4(x^2 - 5x - 6) \)**

As we found just above:
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]

This also simplifies to \( 4x^2 - 20x - 24 \), which matches.

Based on our simplifications, the two expressions that produce the trinomial \( 4x^2 - 20x - 24 \) are:

- \( 4(x - 6)(x + 1) \)
- \( 4(x^2 - 5x - 6) \)

Thus, the correct selections are:

- **\( 4(x - 6)(x + 1) \)**
- **\( 4(x^2 - 5x - 6) \)**