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Factor by grouping (sometimes called the ac-method). 6x -7x-5

Factor by grouping (sometimes called the ac-method). 6x -7x-5

Algebra and Trigonometry (6th Edition)
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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**Factor by grouping (sometimes called the ac-method)** Given quadratic equation: \[ 6x^2 - 7x - 5 \] First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization. ### Form: - ( ) \( 6x^2 + \boxed{} x + \boxed{} x - 5 \) - ( ) \( 6x^2 + \boxed{} x - \boxed{} x - 5 \) - ( ) \( 6x^2 - \boxed{} x + \boxed{} x - 5 \) - ( ) \( 6x^2 - \boxed{} x - \boxed{} x - 5 \) ### Factorization: \[ 6x ( \boxed{}) (x + \boxed{}) - 5( x +\boxed{}) \] ### Explanation of Forms: - The first form represents the case when both terms involving 'x' that split the middle term have positive signs. - The second form represents the case when one term involving 'x' that splits the middle term is positive and the other is negative. - The third form represents the case when one term involving 'x' that splits the middle term is negative and the other is positive. - The fourth form represents the case when both terms involving 'x' that split the middle term have negative signs.
Transcribed Image Text:**Factor by grouping (sometimes called the ac-method)** Given quadratic equation: \[ 6x^2 - 7x - 5 \] First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization. ### Form: - ( ) \( 6x^2 + \boxed{} x + \boxed{} x - 5 \) - ( ) \( 6x^2 + \boxed{} x - \boxed{} x - 5 \) - ( ) \( 6x^2 - \boxed{} x + \boxed{} x - 5 \) - ( ) \( 6x^2 - \boxed{} x - \boxed{} x - 5 \) ### Factorization: \[ 6x ( \boxed{}) (x + \boxed{}) - 5( x +\boxed{}) \] ### Explanation of Forms: - The first form represents the case when both terms involving 'x' that split the middle term have positive signs. - The second form represents the case when one term involving 'x' that splits the middle term is positive and the other is negative. - The third form represents the case when one term involving 'x' that splits the middle term is negative and the other is positive. - The fourth form represents the case when both terms involving 'x' that split the middle term have negative signs.
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