Algebra 2 worksheet for factoring polynomials, featuring 25 problems with instructions to factor completely or use GCF first, with a reminder to verify answers by multiplying factors.

1) 6xy + 8xy² = 2xy(3 + 4y)
2) -12x³y⁴ - 18xy⁵ - 30xy⁶ = -6xy⁴(2x² + 3y + 5y²)
3) 21x⁶y⁵z⁴ - 14x⁴y⁵z⁴ + 7x³y⁵z⁴ = 7x³y⁵z⁴(3x³ - 2x + 1)
4) x² - 49 = (x - 7)(x + 7)
5) 9a² - 16b² = (3a - 4b)(3a + 4b)
6) b⁴ - 16 = (b² - 4)(b² + 4) = (b - 2)(b + 2)(b² + 4)
7) 9x⁴ - 25y¹⁶ = (3x² - 5y⁸)(3x² + 5y⁸)
8) 49r⁴ - 36s⁶ = (7r² - 6s³)(7r² + 6s³)
9) a³ - 27 = (a - 3)(a² + 3a + 9)
10) x³ + 125 = (x + 5)(x² - 5x + 25)
11) x³ + 1 = (x + 1)(x² - x + 1)
12) x³ - 64 = (x - 4)(x² + 4x + 16)
13) 8x³ + 125y³ = (2x + 5y)(4x² - 10xy + 25y²)
14) x³ - 1 = (x - 1)(x² + x + 1)
15) 27x³ - 8y³ = (3x - 2y)(9x² + 6xy + 4y²)
16) 8b³ + 1 = (2b + 1)(4b² - 2b + 1)
17) a⁶ - 8y³ = (a² - 2y)(a⁴ + 2a²y + 4y²)
18) 27x¹² - 8y¹⁵ = (3x⁴ - 2y⁵)(9x⁸ + 6x⁴y⁵ + 4y¹⁰)
19) 8x¹² + 1 = (2x⁴ + 1)(4x⁸ - 2x⁴ + 1)
20) 64x³ - 24y³ = 8(8x³ - 3y³) = 8(2x - ∛3y)(4x² + 2x∛3y + ∛9y²) — Note: This is not factorable over integers as written. Assuming typo, if meant 64x³ - 27y³: (4x - 3y)(16x² + 12xy + 9y²)
21) 2x⁶ - 18x = 2x(x⁵ - 9)
22) 20m⁵ - 5p² = 5(4m⁵ - p²) — Not factorable further over integers.
23) 2x⁴ - 16 = 2(x⁴ - 8) — Not factorable over integers.
24) 3x² - 81x = 3x(x - 27)
25) 2x³ - 250 = 2(x³ - 125) = 2(x - 5)(x² + 5x + 25)
26) x² + 8x + 12 = (x + 2)(x + 6)