Question

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

4(x−6)(x+1)
4 open paren x minus 6 close paren open paren x plus 1 close paren

−4(x^2+5x+6)
negative 4 times open paren x squared plus 5 x plus 6 close paren

4(x^2−5x−6)
4 times open paren x squared minus 5 x minus 6 close paren

4(x^2−20x−24)
4 times open paren x squared minus 20 x minus 24 close paren
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Answer 1

To determine which expressions produce the trinomial \(4x^2 - 20x - 24\), we can simplify each of the provided options and see if they yield the same expression.

1. **Option 1:** \(4(x - 6)(x + 1)\)
\[
= 4(x^2 + x - 6x - 6)
= 4(x^2 - 5x - 6)
= 4x^2 - 20x - 24
\]
**This option works.**

2. **Option 2:** \(-4(x^2 + 5x + 6)\)
\[
= -4x^2 - 20x - 24
\]
**This option does not work.** It yields an expression with a negative leading coefficient.

3. **Option 3:** \(4(x^2 - 5x - 6)\)
\[
= 4x^2 - 20x - 24
\]
**This option works.**

4. **Option 4:** \(4(x^2 - 20x - 24)\)
\[
= 4x^2 - 80x - 96
\]
**This option does not work.**

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

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