Factoring Quadratic Equations and GCF

The video tutorial covers solving quadratic equations by factoring. It begins with an introduction to the concept and various methods such as the greatest common factor (GCF), difference of squares, and factoring trinomials. Several examples are provided to illustrate these techniques, emphasizing the importance of setting equations to zero and solving for x. The tutorial concludes with a complex example and a summary of the key points discussed.

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

• Set the equation equal to zero

• Multiply all terms by a constant

• Add a constant to both sides

• Divide all terms by the leading coefficient

How do you solve for x after factoring a quadratic equation?

• Set each factor equal to zero and solve

• Divide the factors by the leading coefficient

• Multiply the factors together

• Add the factors together

When factoring using the GCF, what should you do after identifying the GCF?

• Add the GCF to each term

• Multiply the GCF by the constant term

• Divide each term by the GCF

• Set the GCF equal to zero

What is the GCF of the terms in the equation 4x^2 - 8x?

• 8

• x

• 4

• 2

In the difference of squares method, what form do the factors take?

• (x + a)(x - b)

• (x - a)(x + a)

• (x - a)(x - a)

• (x + a)(x + a)

What is the result of factoring x^2 - 4 using the difference of squares?

• (x - 4)(x + 4)

• (x - 2)(x + 2)

• (x + 2)(x + 2)

• (x - 2)(x - 2)

What is the solution set for the equation 3x^2 - 5 = 0 after factoring?

• {5/3, -5/3}

• {3, -3}

• {5, -5}

• {0, 5/3}

What is the solution set for the equation (x - 7)(x - 3) = 0?

• {0, 7}

• {7, 3}

• {-7, -3}

• {3, -3}

What should you do if a quadratic equation is not initially set to zero?

• Divide all terms by the leading coefficient

• Multiply all terms by a constant

• Use inverse operations to set it to zero

• Add a constant to both sides

What is the solution set for the equation (x + 5)^2 = 0?

• {5}

• {-5}

• {0}

• {-5, 5}