Solve with difference of two cubes, find all the zeros, linear factors

The video tutorial explains the process of factoring the difference and sum of cubes using specific formulas. It covers finding zeros of cubic equations by taking cube roots and applying the quadratic formula for non-factorable equations. The tutorial also demonstrates simplifying radicals and finding imaginary zeros, followed by writing linear factorization from the zeros. A practice problem is provided to reinforce the concepts.

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)

When finding the zeros of a cubic expression, what is the first step?

• Factor the expression completely

• Simplify the radicals

• Take the cube root of each term

• Apply the quadratic formula

Which formula is used when an expression is non-factorable?

• Radical formula

• Cubic formula

• Quadratic formula

• Linear formula

How can sqrt(12) be simplified?

• 2 sqrt(3)

• 4 sqrt(3)

• 6 sqrt(2)

• 3 sqrt(2)

What is the result of dividing 2 into the expression -2 ± 2i sqrt(3) / 2?

• -1 ± i sqrt(3)

• -1 ± 2i sqrt(3)

• -2 ± i sqrt(3)

• -2 ± 2i sqrt(3)

What is the purpose of linear factorization?

• To simplify radicals

• To apply the quadratic formula

• To find the cube root of a polynomial

• To express a polynomial as a product of linear factors

In the expression X^3 + 27, what is the first step to factor it?

• Use the sum of cubes formula

• Apply the quadratic formula

• Simplify the radicals

• Find the linear factors