Quadratic Equations: Factoring and Solving

The video tutorial explains how to factor and solve quadratic equations by emphasizing the importance of identifying and factoring out the greatest common factor (GCF) first. It provides two examples: the first demonstrates factoring a quadratic equation with a GCF, and the second shows how to factor a quadratic as a perfect square trinomial. The tutorial highlights the simplification process and the importance of recognizing perfect squares, concluding with a brief mention of future examples.

What is the first step in solving a quadratic equation by factoring?

• Completing the square

• Factoring out the greatest common factor

• Using the quadratic formula

• Finding the roots

In the equation 3x^2 + 15x + 18 = 0, what is the greatest common factor?

• 3

• 18

• 5

• 15

After factoring out the greatest common factor in the first example, what is the resulting equation?

• 3x^2 + 15x + 6 = 0

• x^2 + 15x + 18 = 0

• 3x^2 + 5x + 6 = 0

• x^2 + 5x + 6 = 0

What are the solutions for the equation (x + 3)(x + 2) = 0?

• x = 3, x = 2

• x = -3, x = -2

• x = 3, x = -2

• x = -3, x = 2

In the second example, what is the greatest common factor of 8x^2 - 72x + 162?

• 6

• 4

• 8

• 2

What is the resulting equation after factoring out the greatest common factor in the second example?

• 8x^2 - 36x + 81 = 0

• 4x^2 - 36x + 81 = 0

• 4x^2 - 72x + 81 = 0

• 8x^2 - 72x + 162 = 0

What are the factors of the perfect square trinomial 4x^2 - 36x + 81?

• (2x - 9)(2x - 9)

• (4x - 9)(x - 9)

• (4x + 9)(x + 9)

• (2x + 9)(2x + 9)

What is the solution for the equation (2x - 9)^2 = 0?

• x = -4.5

• x = -9

• x = 4.5

• x = 9

What does it mean when a solution has a multiplicity of 2?

• The solution is a fraction

• The solution is a complex number

• The solution is incorrect

• The solution is repeated twice

What is the term used to describe a solution that appears twice?

• Double root

• Complex root

• Fractional root

• Imaginary root