Question

When simplified, which expressions produce the trinomial 4x2−20x−24
? Select the TWO that apply.(2 points)
Responses

−4(x2+5x+6)
negative 4 times open paren x squared plus 5 x plus 6 close paren

4(x2−5x−6)
4 times open paren x squared minus 5 x minus 6 close paren

4(x2−20x−24)
4 times open paren x squared minus 20 x minus 24 close paren

4(x−6)(x+1)

Answer 1

To determine which expressions produce the trinomial \( 4x^2 - 20x - 24 \), let’s simplify each expression and see if any of them equal that trinomial.

1. **First Expression: \(-4(x^2 + 5x + 6)\)**
Simplifying this:
\[
-4(x^2 + 5x + 6) = -4x^2 - 20x - 24
\]
This does **not** match the trinomial since all the signs are opposite.

2. **Second Expression: \(4(x^2 - 5x - 6)\)**
Simplifying this:
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
This does match the trinomial.

3. **Third Expression: \(4(x^2 - 20x - 24)\)**
Simplifying this:
\[
4(x^2 - 20x - 24) = 4x^2 - 80x - 96
\]
This does **not** match the trinomial.

4. **Fourth Expression: \(4(x - 6)(x + 1)\)**
First, we need to expand this:
\[
4((x - 6)(x + 1)) = 4(x^2 + x - 6x - 6) = 4(x^2 - 5x - 6)
\]
And from above, we know:
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
This does match the trinomial as well.

Therefore, the two expressions that produce the trinomial \( 4x^2 - 20x - 24 \) are:

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