Question

When simplified, which expressions produce the
trinomial 4x2 - 20x - 24? Select the TWO that apply.
(2 points)
4 (22 – 52 – 6)
-
4 (x − 6) (x + 1)
4 (x² - 20x - 24)
−4 (22 +5 +6)

Answer 1

To determine which expressions produce the trinomial \( 4x^2 - 20x - 24 \) when simplified, we can simplify each expression and check if it matches the trinomial.

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

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

This expression simplifies to \( 4x^2 - 20x - 24 \), so it is correct.

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

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

This does not match \( 4x^2 - 20x - 24 \).

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

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

This does not match \( 4x^2 - 20x - 24 \).

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

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

This does not match \( 4x^2 - 20x - 24 \).

After checking all expressions, the two that produce the trinomial \( 4x^2 - 20x - 24 \) when simplified is:

- **\( 4(x^2 - 5x - 6) \)**
- None of the others match.

Final answer: **Only the first expression \( 4(x^2 - 5x - 6) \) is correct.**