Question 9 • Common Core Algebra I B-IC
A, C, and D factor by grouping: A = (7x + 2)(x − 5), C = (2x − 3)(5x² + 4), and D = (2x² + 7)(6x² + 2). For B, reducing its coefficients modulo 7 gives 2x³ + 4x² + 3x + 2, which has no root among 0, 1, 2, 3, 4, 5, or 6. A cubic that factors must have a linear factor and therefore a root, so B is prime.
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