Explanation Property used: Zero factor property: If a ⋅ b = 0 then a = 0 or b = 0 . Calculation: Obtain the factor of 3 x 2 − 17 x + 10 . The possible factors of 3 x 2 is ( 3 x ) ⋅ ( x ) and the possible factors of 10 are − 10 ( − 1 ) , 10 ( 1 ) , − 5 ( − 2 ) and 5 ( 2 ) . Possible factors Sum of products of outer and inner Terms ( 3 x − 10 ) ( x − 1 ) − 3 x − 10 x = − 13 x ( 3 x + 10 ) ( x + 1 ) 3 x + 10 x = 13 x ( 3 x − 5 ) ( x − 2 ) − 6 x − 5 x = − 11 x ( 3 x + 5 ) ( x + 2 ) 6 x + 5 x = 11 x ( 3 x − 1 ) ( x − 10 ) − 30 x − x = − 31 x ( 3 x + 1 ) ( x + 10 ) 30 x + x = 31 x ( 3 x − 2 ) ( x − 5 ) − 15 x − 2 x = − 17 x ( 3 x + 2 ) ( x + 5 ) 15 x + 2 x = 17 x From the above table, the correct middle term is 17 x and the required factors are ( 3 x − 2 ) and ( x − 5 )

A Survey of Mathematics with Applications (10th Edition) - Standalone book

10th Edition

ISBN: 9780134112107

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 6, Problem 81RE

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To solve: The equation 3x2−17x+10=0 by factoring.

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Chapter 6, Problem 80RE

Chapter 6, Problem 82RE

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A Survey of Mathematics with Applications (10th Edition) - Standalone book

Ch. 6.1 - A letter of the alphabet used to represent numbers...Ch. 6.1 - Prob. 2E Ch. 6.1 - A collection of variables, numbers, grouping...Ch. 6.1 - The number or numbers that replace the variable to...Ch. 6.1 - The parts that are added or subtracted in an...Ch. 6.1 - Terms that have the same variables with the same...Ch. 6.1 - The numerical part of a term is called its...Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The equation 3 x 2 − 17 x + 10 = 0 by factoring.

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