Which examples illustrate that a trinomial can be the product of two binomials? (Select all that apply.) 0 2а? - 4а - 6 %3D 2 (а2 — 2а — 3) Оа?+ 5а+63 (а +2) (а+3) О За? + 9а - 6 3 3(а? + За — 2) O a² + 2a + 4 = a² + a + a + 4 Da2+а — 20 3 (а+5) (а — 4)
Which examples illustrate that a trinomial can be the product of two binomials? (Select all that apply.) 0 2а? - 4а - 6 %3D 2 (а2 — 2а — 3) Оа?+ 5а+63 (а +2) (а+3) О За? + 9а - 6 3 3(а? + За — 2) O a² + 2a + 4 = a² + a + a + 4 Da2+а — 20 3 (а+5) (а — 4)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question:**
Which examples illustrate that a trinomial can be the product of two binomials? (Select all that apply.)
**Options:**
1. \( \square \, 2a^2 - 4a - 6 = 2 \left(a^2 - 2a - 3 \right) \)
2. \( \square \, a^2 + 5a + 6 = (a + 2)(a + 3) \)
3. \( \square \, 3a^2 + 9a - 6 = 3 \left(a^2 + 3a - 2 \right) \)
4. \( \square \, a^2 + 2a + 4 = a^2 + a + a + 4 \)
5. \( \square \, a^2 + a - 20 = (a + 5)(a - 4) \)
**Explanation:**
To determine which trinomials can be the product of two binomials, we must factorize them.
1. \( 2a^2 - 4a - 6 \) cannot be factorized straightforwardly into the product of two binomials. Simplifying the right side: \( 2(a^2 - 2a - 3) \), reveals:
\[
2(a^2 - 2a - 3) = 2(a - 3)(a + 1) = 2a^2 - 6a + 2a - 6
\]
Hence, \( 2a^2 - 4a - 6 \neq 2(a^2 - 2a - 3) \).
2. \( a^2 + 5a + 6 \) is indeed the product of two binomials:
\[
(a + 2)(a + 3) = a^2 + 3a + 2a + 6 = a^2 + 5a + 6
\]
3. \( 3a^2 + 9a - 6 \) can be factored as:
\[
3(a^2 + 3a - 2) = 3(a + 3)(a - 1) = 3a^2 + 9a -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b91f986-cff4-42a8-8faf-14c1255b04a2%2F5266f226-a1db-4d78-8fe6-f382c980344e%2Fbhx1dxn_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Which examples illustrate that a trinomial can be the product of two binomials? (Select all that apply.)
**Options:**
1. \( \square \, 2a^2 - 4a - 6 = 2 \left(a^2 - 2a - 3 \right) \)
2. \( \square \, a^2 + 5a + 6 = (a + 2)(a + 3) \)
3. \( \square \, 3a^2 + 9a - 6 = 3 \left(a^2 + 3a - 2 \right) \)
4. \( \square \, a^2 + 2a + 4 = a^2 + a + a + 4 \)
5. \( \square \, a^2 + a - 20 = (a + 5)(a - 4) \)
**Explanation:**
To determine which trinomials can be the product of two binomials, we must factorize them.
1. \( 2a^2 - 4a - 6 \) cannot be factorized straightforwardly into the product of two binomials. Simplifying the right side: \( 2(a^2 - 2a - 3) \), reveals:
\[
2(a^2 - 2a - 3) = 2(a - 3)(a + 1) = 2a^2 - 6a + 2a - 6
\]
Hence, \( 2a^2 - 4a - 6 \neq 2(a^2 - 2a - 3) \).
2. \( a^2 + 5a + 6 \) is indeed the product of two binomials:
\[
(a + 2)(a + 3) = a^2 + 3a + 2a + 6 = a^2 + 5a + 6
\]
3. \( 3a^2 + 9a - 6 \) can be factored as:
\[
3(a^2 + 3a - 2) = 3(a + 3)(a - 1) = 3a^2 + 9a -
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