Introduction to Factoring Polynomials

x⁴ - 36

• (x + 6)(x - 6)
• (x + 3)(x - 3)(x² + 6)
• cannot be factored
• (x² - 6)(x²+ 6)

k³ - 27

• (k - 3)³
• (k - 3)(k² + 3k + 9)
• (k + 3)(k² - 3k + 9)
• (k - 3)(k² - 3k + 9)

x⁴ - 81

• (x² - 9)(x² + 9)
• (x - 3)²(x + 3)²
• (x - 3)(x + 3)(x² + 9)
• (x - 3)⁴

16x⁴ - 49

• (4x² - 7)(4x² + 7)
• (4x - 7)(4x + 7)
• (2x - 7)(2x + 7)(4x² + 7)
• cannot be factored

10x⁵y - 40xy³

• 10xy(x⁴ - 4y²)
• cannot be factored
• 10xy(x² - 2y)(x² + 2y)
• (x² - 2y)(x² + 2y)

250m³ +  54

• 2(5m + 3)(25m² - 15m + 9)
• 2(125m³ + 27)
• (5m + 3)(25m² - 15m + 9)
• cannot be factored

a⁵b - 64 ab

• ab(a⁴ - 64)
• ab(a² - 8)(a² + 8)
• ab(a - 4)(a² + 4a  + 16)
• ab(a - 2)²(a + 2)²

k⁴ - 10k² - 39

• (k² - 13)(k² + 3)
• (k - 13)(k + 3)
• (k² + 15)(k² - 3)
• (k + 13)(k - 3)

4w⁴ + 16w² + 15

• (w² + 10)(w² + 6)
• (2w²+ 5)(2w² + 3)
• (w² + 15)(4w² + 1)
• (2w + 5)(2w + 3)

2n³ + 7n² - 2n - 7

• cannot be factored
• (n - 1)²(2n + 7)
• (n² - 1)(2n + 7)
• (n + 1)(n - 1)(2n + 7)