Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.2: Multiplying A Polynomial By A Monomial
Problem 50HP
Related questions
Question

Transcribed Image Text:**Problem 4: Factor Quadratic Expression**
Expression: \( 6x^2 + x - 12 \)
**Instructions:** Factor the quadratic expression by grouping.
### Explanation:
To factor by grouping, follow these steps:
1. **Multiply**: Multiply the coefficient of \(x^2\) (which is 6) by the constant term (-12), resulting in -72.
2. **Find Two Numbers**: Identify two numbers that multiply to -72 and add to the coefficient of \(x\) (which is 1). These numbers are 9 and -8.
3. **Rewrite the Middle Term**: Rewrite \(x\) as \(9x - 8x\).
- Expression Becomes: \(6x^2 + 9x - 8x - 12\)
4. **Group Terms**: Group the terms into two pairs.
- Group 1: \( (6x^2 + 9x) \)
- Group 2: \( (-8x - 12) \)
5. **Factor Each Group**:
- Group 1: Factor out \(3x\), resulting in \(3x(2x + 3)\).
- Group 2: Factor out \(-4\), resulting in \(-4(2x + 3)\).
6. **Combine**: Notice the common factor \(2x + 3\).
- Final Factored Form: \((3x - 4)(2x + 3)\)
By grouping, we have factored the quadratic expression successfully.
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