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
![### Factoring a Quadratic Expression
The task is to factor the quadratic expression given below:
\[ x^2 - 15x + 36 \]
The equation is written in standard quadratic form:
\[ ax^2 + bx + c \]
where \( a = 1 \), \( b = -15 \), and \( c = 36 \).
To factor the quadratic expression, you need to find two numbers that multiply to \( c \) (36) and add up to \( b \) (-15). After determining these numbers, the quadratic can be written as a product of two binomials.
### Solution Process:
1. Identify the quadratic expression: \( x^2 - 15x + 36 \).
2. Determine factors of 36 that sum up to -15.
3. Rewrite the quadratic expression as a product of binomials.
### Factorization:
Once the appropriate numbers are found, they allow you to complete the factorization:
\[ (x - a)(x - b) \]
where \( a \) and \( b \) are the numbers determined from the process above.
Note: This section doesn't solve the problem but guides the process. Fill in the solution using the numbers found from the steps described.
\( x^2 - 15x + 36 = \) [Input solution in the box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F841a23ff-64ca-4d99-a92f-2adfa7b3fe4f%2F3d4d380d-ff39-4864-baff-bf4f13b1f84a%2F4xztbiyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Factoring a Quadratic Expression
The task is to factor the quadratic expression given below:
\[ x^2 - 15x + 36 \]
The equation is written in standard quadratic form:
\[ ax^2 + bx + c \]
where \( a = 1 \), \( b = -15 \), and \( c = 36 \).
To factor the quadratic expression, you need to find two numbers that multiply to \( c \) (36) and add up to \( b \) (-15). After determining these numbers, the quadratic can be written as a product of two binomials.
### Solution Process:
1. Identify the quadratic expression: \( x^2 - 15x + 36 \).
2. Determine factors of 36 that sum up to -15.
3. Rewrite the quadratic expression as a product of binomials.
### Factorization:
Once the appropriate numbers are found, they allow you to complete the factorization:
\[ (x - a)(x - b) \]
where \( a \) and \( b \) are the numbers determined from the process above.
Note: This section doesn't solve the problem but guides the process. Fill in the solution using the numbers found from the steps described.
\( x^2 - 15x + 36 = \) [Input solution in the box]
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