Learn How to Solve a Polynomial Using the Difference of Two Cubes

The video tutorial reviews the previous class's topic on factoring, focusing on the difference of two cubes. It explains how to factor using the greatest common factor (GCF) and identifies the values of A and B for the factoring formula. The tutorial then simplifies the expression and solves the equation using the quadratic formula, highlighting the importance of finding all solutions, including complex ones.

What is the factored form of a difference of two cubes?

• (a - b)(a^2 - ab + b^2)

• (a + b)(a^2 + ab + b^2)

• (a + b)(a^2 - ab + b^2)

• (a - b)(a^2 + ab + b^2)

Why is it important to factor out the greatest common factor (GCF) before identifying cube numbers?

• It eliminates the need for further factoring.

• It changes the expression into a quadratic form.

• It increases the degree of the polynomial.

• It simplifies the expression and makes cube numbers more apparent.

How do you determine the value of 'a' in the expression a^3 = x^3?

• By taking the cube root of x^3

• By dividing x^3 by 3

• By taking the square root of x^3

• By multiplying x by itself three times

What is the next step after substituting the values of 'a' and 'b' into the factored form formula?

• Divide the expression by the GCF.

• Add the expression to another polynomial.

• Multiply the expression by a constant.

• Set the expression equal to zero and solve for the variable.

What property allows us to set each factor of a polynomial equal to zero?

• Zero Product Property

• Distributive Property

• Commutative Property

• Associative Property

When a quadratic equation is not factorable, which method can be used to find its solutions?

• Quadratic formula

• Graphing

• Long division

• Synthetic division

What type of solutions are obtained when using the quadratic formula on a polynomial with a negative discriminant?

• Integer solutions

• Complex solutions

• Real solutions

• Rational solutions