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4. 6x²+x-12 Factor by grouping

4. 6x²+x-12 Factor by grouping

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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
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Question
**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.
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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