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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![## Completing the Factorization
The given expression is:
\[ -a^2 - a + 56 \]
We need to factorize this expression. Let's start by rewriting it in the form of minus a factorization of a quadratic expression.
\[ -a^2 - a + 56 = -(a^2 - \square a + 56) \]
Next, we need to determine the values that fill in the blanks. The central step will be to fill in the correct middle term to help work towards the factorization.
From the given choices in the dropdown, we choose the correct operations and terms to complete the factorization.
Finally, the factorized form is given as:
\[ = -(a + 8)(a - 7) \]
This factorization splits the middle term \(-a\) appropriately and uses the correct factors of 56 that add up to -1, resulting in \(a + 8\) and \(a - 7\).
So, the correct complete factorization is:
\[ -a^2 - a + 56 = -(a + 8)(a - 7) \]
This is how the quadratic expression is fully factorized using suitable terms and operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b91f986-cff4-42a8-8faf-14c1255b04a2%2Fe99090d8-2ff6-4c0c-8f42-a1d3bd1f7277%2F7ro87e9_processed.png&w=3840&q=75)
Transcribed Image Text:## Completing the Factorization
The given expression is:
\[ -a^2 - a + 56 \]
We need to factorize this expression. Let's start by rewriting it in the form of minus a factorization of a quadratic expression.
\[ -a^2 - a + 56 = -(a^2 - \square a + 56) \]
Next, we need to determine the values that fill in the blanks. The central step will be to fill in the correct middle term to help work towards the factorization.
From the given choices in the dropdown, we choose the correct operations and terms to complete the factorization.
Finally, the factorized form is given as:
\[ = -(a + 8)(a - 7) \]
This factorization splits the middle term \(-a\) appropriately and uses the correct factors of 56 that add up to -1, resulting in \(a + 8\) and \(a - 7\).
So, the correct complete factorization is:
\[ -a^2 - a + 56 = -(a + 8)(a - 7) \]
This is how the quadratic expression is fully factorized using suitable terms and operations.
![### Complete the factorization.
\[
-a^2 - a + 56 = -(a^2 - \Box a + \Box)
\]
\[
= -(a + 8) (\Box)
\]
The text is providing steps to complete the factorization of a given quadratic expression. Here is a detailed explanation:
1. The original expression given is \( -a^2 - a + 56 \).
2. The first step involves factoring out the negative sign from the quadratic expression:
\[ -a^2 - a + 56 = -(a^2 - \Box a + \Box), \]
where \(\Box\) denotes the missing terms that need to be filled so that the expression inside the parentheses remains equivalent to \( a^2 - a + 56 \).
3. The next line transforms the expression further by factoring it into the product of two binomials:
\[ = -(a + 8)(\Box). \]
The boxes (\(\Box\)) represent the values that need to be identified to complete the factoring process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b91f986-cff4-42a8-8faf-14c1255b04a2%2Fe99090d8-2ff6-4c0c-8f42-a1d3bd1f7277%2Fqdq3o9p_processed.png&w=3840&q=75)
Transcribed Image Text:### Complete the factorization.
\[
-a^2 - a + 56 = -(a^2 - \Box a + \Box)
\]
\[
= -(a + 8) (\Box)
\]
The text is providing steps to complete the factorization of a given quadratic expression. Here is a detailed explanation:
1. The original expression given is \( -a^2 - a + 56 \).
2. The first step involves factoring out the negative sign from the quadratic expression:
\[ -a^2 - a + 56 = -(a^2 - \Box a + \Box), \]
where \(\Box\) denotes the missing terms that need to be filled so that the expression inside the parentheses remains equivalent to \( a^2 - a + 56 \).
3. The next line transforms the expression further by factoring it into the product of two binomials:
\[ = -(a + 8)(\Box). \]
The boxes (\(\Box\)) represent the values that need to be identified to complete the factoring process.
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