Factor by first looking for a greatest common factor. 16x²2-36 16x²-36= 4(2x + 3) (2x - 3)
Factor by first looking for a greatest common factor. 16x²2-36 16x²-36= 4(2x + 3) (2x - 3)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![### Factoring by First Looking for a Greatest Common Factor
To factor the given polynomial expression, we start by identifying the greatest common factor (GCF).
**Expression:**
\[ 16x^2 - 36 \]
**Step-by-Step Solution:**
1. **Identify the GCF**:
The greatest common factor of \(16x^2\) and \(-36\) is 4.
2. **Factor Out the GCF**:
Divide each term by the GCF and factor it out:
\[ 16x^2 - 36 = 4(4x^2 - 9) \]
3. **Recognize Further Factoring (Difference of Squares)**:
The expression inside the parentheses, \(4x^2 - 9\), is a difference of squares. Recall that:
\[ a^2 - b^2 = (a + b)(a - b) \]
Here, \(4x^2\) is \((2x)^2\) and \(9\) is \(3^2\). So:
\[ 4x^2 - 9 = (2x + 3)(2x - 3) \]
4. **Combine All Factors**:
Substitute back to get the fully factored expression:
\[ 16x^2 - 36 = 4(2x + 3)(2x - 3) \]
**Final Factored Form:**
\[ 16x^2 - 36 = 4(2x + 3)(2x - 3) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b70f989-f4fe-4180-9465-a46932af6785%2F077334e4-834e-4806-8cdd-9335d5eeb779%2F9p3y6e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Factoring by First Looking for a Greatest Common Factor
To factor the given polynomial expression, we start by identifying the greatest common factor (GCF).
**Expression:**
\[ 16x^2 - 36 \]
**Step-by-Step Solution:**
1. **Identify the GCF**:
The greatest common factor of \(16x^2\) and \(-36\) is 4.
2. **Factor Out the GCF**:
Divide each term by the GCF and factor it out:
\[ 16x^2 - 36 = 4(4x^2 - 9) \]
3. **Recognize Further Factoring (Difference of Squares)**:
The expression inside the parentheses, \(4x^2 - 9\), is a difference of squares. Recall that:
\[ a^2 - b^2 = (a + b)(a - b) \]
Here, \(4x^2\) is \((2x)^2\) and \(9\) is \(3^2\). So:
\[ 4x^2 - 9 = (2x + 3)(2x - 3) \]
4. **Combine All Factors**:
Substitute back to get the fully factored expression:
\[ 16x^2 - 36 = 4(2x + 3)(2x - 3) \]
**Final Factored Form:**
\[ 16x^2 - 36 = 4(2x + 3)(2x - 3) \]
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