Learn how to solve a polynomial using the difference of two cubes and quadratic formula

The video tutorial covers the concepts of factoring the difference of cubes, specifically a^3 - b^3, and solving equations using the zero product property and the quadratic formula. It begins with an introduction to cubes, followed by a detailed explanation of factoring a^3 - b^3. The tutorial then demonstrates solving the equation using the factored form and applying the zero product property. Finally, it explores the use of the quadratic formula to find solutions, including complex numbers.

What is the general formula for factoring the difference of two cubes?

• a^3 - b^3 = (a + b)(a^2 + ab + b^2)

• a^3 - b^3 = (a - b)(a^2 - ab + b^2)

• a^3 - b^3 = (a + b)(a^2 - ab + b^2)

• a^3 - b^3 = (a - b)(a^2 + ab + b^2)

How do you determine the value of B in the expression a^3 - b^3?

• By taking the square root of b^3

• By taking the cube root of b^3

• By dividing b^3 by 3

• By multiplying b^3 by 3

What is the next step after factoring the expression a^3 - b^3?

• Divide the terms by a constant

• Multiply the terms by a constant

• Add the terms together

• Solve the equation using the Zero Product Property

What property is used to solve the equation when the product of two factors is set to zero?

• Zero Product Property

• Associative Property

• Distributive Property

• Commutative Property

What method can be used to solve a quadratic equation if it cannot be factored?

• Graphing

• Completing the square

• Using the quadratic formula

• Both completing the square and using the quadratic formula

What is the nature of the solutions when the discriminant of a quadratic equation is negative?

• Two real solutions

• No solution

• One real solution

• Two complex solutions

How many total solutions are there for a cubic equation with a power of 3?

• Four

• One

• Two

• Three