78714
AssignmentMultiple Choice

Factoring Polynomials: Double Grouping

Question 78714 • Common Core Algebra I B-IC

Which polynomial has (3x + 2) as a binomial factor?

Answer
A
6x3 + 3x2 + 4x + 2
B
12x2 + 15x + 8x + 10
C
18x3 – 12x2 + 9x – 6
D
21x4 + 7x3 + 6x + 2

Explanation

Group the terms in choice B: 12x² + 15x + 8x + 10 = 3x(4x + 5) + 2(4x + 5). Factoring out the shared binomial gives (3x + 2)(4x + 5), so (3x + 2) is a factor. The correct choice is B, the polynomial 12x² + 15x + 8x + 10.

AI-written and checked against the verified answer.

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