Factoring Quadratic Equations

The video tutorial explains how to solve quadratic equations by factoring. It begins with an introduction to the zero product property, which is essential for understanding how factoring can be used to find the solutions of quadratic equations. The tutorial outlines the steps for solving quadratics by factoring, including moving all terms to one side of the equation, factoring, and setting each factor equal to zero. Several examples are provided, demonstrating different factoring techniques such as using the greatest common factor (GCF), difference of squares, and trinomials. The video also covers more complex examples, including adjusting equations to make them solvable by factoring.

What does the zero product property state?

• If a product of two numbers is zero, one or both of the numbers must be zero.

• If a product of two numbers is zero, both numbers must be non-zero.

• If a product of two numbers is zero, both numbers must be positive.

• If a product of two numbers is zero, one number must be negative.

What is the first step in solving quadratics by factoring?

• Set both factors equal to zero.

• Factor the equation.

• Move all terms to the same side of the equation.

• Solve for x.

In the first example, what is the GCF of 4x^2 - 2x?

• x

• 2x

• 2

• 4

What is the next step after factoring the equation?

• Check for GCF.

• Move all terms to the same side.

• Set both factors equal to zero.

• Solve for x.

In the example 4x^2 - 9 = 0, what are the factors?

• 2x + 9 and 2x - 9

• x + 3 and x - 3

• 4x + 9 and 4x - 9

• 2x + 3 and 2x - 3

What is the solution for x in the equation 4x^2 - 9 = 0?

• x = 3/2 and x = -3/2

• x = 1/2 and x = -1/2

• x = 2 and x = -2

• x = 3 and x = -3

In the example x^2 - 9x - 9 = 0, what are the factors?

• x + 3 and x - 3

• x + 2 and x - 4

• x + 9 and x - 1

• x + 1 and x - 9

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

• x = 2 and x = -4

• x = 3 and x = -3

• x = 1 and x = -9

• x = -1 and x = 9

In the example 2x^2 - 5x + 3 = 0, what are the factors?

• x - 2 and 2x - 1

• x - 1 and 2x - 3

• x + 1 and 2x + 3

• x + 2 and 2x + 1

What is the solution for x in the equation 2x^2 - 5x + 3 = 0?

• x = 2 and x = 1/2

• x = 1 and x = 3/2

• x = -1 and x = -3/2

• x = -2 and x = -1/2