Factoring the difference or sum of two cubes

Question

Assignment:

Factoring the Difference or Sum of Two Cubes

Q1. Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. x3 + 2x2 - 5x - 6 , x + 3

Q2. Factor each polynomial completely. u3 = 125 v3

Q3. Factor each polynomial completely, if prime say so. 32a2 + 4a - 6

Q4. Factor each polynomial completely, if prime say so. 9bn3 + 15bn2 - 14bn
 
Q5. Decreasing cube. Each of the three dimensions of a cube with a volume of y3 cubic centimeters is decreased by a whole number of centimeters. 

If a new volume is y³ - 12y² + 54y - 72  cubic centimeters and the new width is  y – 6 centimeters, then what are the new length and height?
   
Solving Quadratic Equations by Factoring

Q6. Solve the equation using zero factor property 2h² - h - 3 = 0

Q7. Solve the equation using zero factor property  2w(4w + 1) = 1

Q8. Solve each equation with repeated or three solutions. m³ + 2m² = 3m = 0

Provide complete and step by step solution for the question and show calculations and use formulas.