Question
When simplified, which expressions produce the trinomial 4x2−20x−24
? Select the TWO that apply.(2 points)
Responses
4(x2−20x−24)
4 times open paren x squared minus 20 x minus 24 close paren
4(x−6)(x+1)
4 open paren x minus 6 close paren open paren x plus 1 close paren
4(x2−5x−6)
4 times open paren x squared minus 5 x minus 6 close paren
−4(x2+5x+6)
? Select the TWO that apply.(2 points)
Responses
4(x2−20x−24)
4 times open paren x squared minus 20 x minus 24 close paren
4(x−6)(x+1)
4 open paren x minus 6 close paren open paren x plus 1 close paren
4(x2−5x−6)
4 times open paren x squared minus 5 x minus 6 close paren
−4(x2+5x+6)
Answers
Answered by
GPT-4o mini
To determine which expressions simplify to the trinomial \(4x^2 - 20x - 24\), we can evaluate each option.
1. **Evaluate \(4(x^2 - 20x - 24)\):**
\[
4(x^2 - 20x - 24) = 4x^2 - 80x - 96
\]
**Not a match.**
2. **Evaluate \(4(x - 6)(x + 1)\):**
\[
4[(x - 6)(x + 1)] = 4(x^2 + x - 6x - 6) = 4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
**Match!**
3. **Evaluate \(4(x^2 - 5x - 6)\):**
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
**Match!**
4. **Evaluate \(-4(x^2 + 5x + 6)\):**
\[
-4(x^2 + 5x + 6) = -4x^2 - 20x - 24
\]
**Not a match.**
Based on these evaluations, the two expressions that produce the trinomial \(4x^2 - 20x - 24\) are:
- \(4(x - 6)(x + 1)\)
- \(4(x^2 - 5x - 6)\)
1. **Evaluate \(4(x^2 - 20x - 24)\):**
\[
4(x^2 - 20x - 24) = 4x^2 - 80x - 96
\]
**Not a match.**
2. **Evaluate \(4(x - 6)(x + 1)\):**
\[
4[(x - 6)(x + 1)] = 4(x^2 + x - 6x - 6) = 4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
**Match!**
3. **Evaluate \(4(x^2 - 5x - 6)\):**
\[
4(x^2 - 5x - 6) = 4x^2 - 20x - 24
\]
**Match!**
4. **Evaluate \(-4(x^2 + 5x + 6)\):**
\[
-4(x^2 + 5x + 6) = -4x^2 - 20x - 24
\]
**Not a match.**
Based on these evaluations, the two expressions that produce the trinomial \(4x^2 - 20x - 24\) are:
- \(4(x - 6)(x + 1)\)
- \(4(x^2 - 5x - 6)\)