Factoring Part 1:  GCF and Grouping

1. Factor the GCF from 7x²y³ + 14x³y + x⁵y⁴

  x²y(7y² + 14x + x³y³)

  7xy(xy² + 2x + x⁴y³)

  xy(7xy² + 14x² + x⁴y³)

2. Factor the GCF from 15a³b³ + 12a⁵ + 6b⁵

  3(5a³b³ + 4a⁵ + 2b⁵)

  3a³(5b³ + 4a² + 2b⁵)

  3b³(5a³ + 4a⁵ + 2b²)

3. Factor by grouping x(4x - 3y) - 2(4x - 3y).

  4x - 3y + x - 2

  (4x - 3y) + (x - 2)

  (4x - 3y)(x - 2)

4. Factor by grouping xy + 4x + 5y + 20

 x(y + 4) + 5(y + 4)

 y(x + 5) + 4(x + 5)

 (x + 5)(y + 4)

5. Factor x² - 5x + 6.

 (x - 6)(x + 1)

 (x + 3)(x + 2)

 (x - 3)(x - 2)

6. Factor  8x² - 18x - 5.

 (2x - 5)(4x + 1)

 (2x + 5)(4x - 1)

 (2x - 5)(4x - 1)

7. Factor x⁴ - 2x² - 15

 (x² - 5)(x² + 3)

  (x² + 5)(x² + 3)

  (x² + 5)(x² - 3)

8. Factor 4x³ - 4x² + 4x + 4

 4x( x² + x + 1)

 4(x³ - x² + x + 1)

  This is a prime polynomial.

9. Factor x² + 3x + 1

  (x + 1)(x + 1)

  (x + 1)(x + 3)

  This is a prime polynomial.