Finding the zeros by factoring using the difference of two cubes

The video tutorial explains the relationship between the difference of two squares and the difference of two cubes. It begins by demonstrating how to factor expressions like X^2 - 9 using the difference of squares formula. The instructor then identifies variables A and B by taking square roots. The lesson progresses to solving equations involving the difference of two cubes, applying the formula a + b * a^2 - ab + b^2. The tutorial concludes with solving quadratic equations using the quadratic formula, highlighting the use of complex numbers for solutions.

What is the factored form of X^2 - 9?

• (X - 2)(X + 4)

• (X - 9)(X + 9)

• (X - 1)(X + 9)

• (X - 3)(X + 3)

In the expression X^3 - 27, what is the value of B?

• 3

• 9

• 27

• 1

Which formula is used for the sum of two cubes?

• a^2 + 2ab + b^2

• a^2 - b^2

• a + b * (a^2 - ab + b^2)

• a^3 - b^3

What is the first step in solving X + 3 = 0 using the zero product property?

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

• Subtract 3 from both sides

Why can't the quadratic X^2 - 3X + 9 = 0 be solved using real numbers?

• It has no real roots

• It is already factored

• It is not a quadratic equation

• It has a negative discriminant

What is the quadratic formula used to solve X^2 - 3X + 9 = 0?

• X = -b ± sqrt(b^2 + 4ac) / 2a

• X = b ± sqrt(b^2 + 4ac) / 2a

• X = -b ± sqrt(b^2 - 4ac) / 2a

• X = b ± sqrt(b^2 - 4ac) / 2a

How is the square root of -27 expressed in terms of complex numbers?

• 3i sqrt(3)

• 3 sqrt(3)

• i sqrt(27)

• sqrt(-27)