78723
AssignmentMultiple Choice

Factoring Polynomials: Double Grouping

Question 78723 • Common Core Algebra I B-IC

Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. What is the resulting expression?

Answer
A
(4x2 + 3)(x2 – 5)
B
(4x2 – 3)(x2 – 5)
C
(4x2 – 5)(x2 + 3)
D
(4x2 + 5)(x2 – 3)

Explanation

Group the terms as (4x⁴ − 20x²) + (−3x² + 15). Factoring each group gives 4x²(x² − 5) − 3(x² − 5), so the common factor is (x² − 5). The result is (4x² − 3)(x² − 5), which is choice B.

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