Answers Algebra I Factoring Polynomials: Double Grouping — QuizQuestion 10

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Factoring Polynomials: Double Grouping — Quiz

Question 10 • Algebra I

Which shows one way to determine the factors of 12 x cubed minus 2 x squared plus 18 x minus 3 by grouping?

Answer

A

2 x squared open paren 6 x minus 1 close paren plus 3 times open paren 6 x minus 1 close paren

B

6 x open paren 2 x squared plus 3 close paren plus 1 times open paren 2 x squared plus 3 close paren

C

6 x open paren 2 x squared minus 3 close paren minus 1 times open paren 2 x squared minus 3 close paren

D

2 x squared open paren 6 x minus 1 close paren minus 3 times open paren 6 x minus 1 close paren

Explanation

Group the polynomial as (12x³ − 2x²) + (18x − 3). Factor each group: 2x²(6x − 1) + 3(6x − 1). Both terms now share the factor (6x − 1), so choice B shows the grouping correctly.

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