Question

When simplified, which expressions produce the trinomial 4x^2−20x−24
? Select the TWO that apply.(2 points)
Responses

−4(x^2+5x+6)

4(x−6)(x+1)

4(x^2−20x−24)

4(x^2−5x−6)

Answer 1

To determine which expressions produce the trinomial \( 4x^2 - 20x - 24 \), we need to simplify each option and see if they match the original expression.

1. **Option 1: \( -4(x^2 + 5x + 6) \)**
- Distributing the -4:
\[
-4(x^2 + 5x + 6) = -4x^2 - 20x - 24
\]
- This does not match \( 4x^2 - 20x - 24 \).

2. **Option 2: \( 4(x - 6)(x + 1) \)**
- First we expand \( (x - 6)(x + 1) \):
\[
(x - 6)(x + 1) = x^2 + x - 6x - 6 = x^2 - 5x - 6
\]
- Now distributing the 4:
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
- This matches our original trinomial.

3. **Option 3: \( 4(x^2 - 20x - 24) \)**
- This simply multiplies the entire expression by 4:
\[
4(x^2 - 20x - 24) = 4x^2 - 80x - 96
\]
- This does not match the original expression.

4. **Option 4: \( 4(x^2 - 5x - 6) \)**
- As shown in step 2, expanding this expression gives:
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
- This also matches the original trinomial.

Thus, the two expressions that produce \( 4x^2 - 20x - 24 \) are:
- \( 4(x - 6)(x + 1) \)
- \( 4(x^2 - 5x - 6) \)