Factoring Quadratic Equations Concepts

The video tutorial explains how to solve a quadratic equation by factoring. It begins by setting one side of the equation to zero, ensuring the degree two term is positive. The process involves adding and subtracting terms to simplify the equation. The next step is factoring the equation by identifying the greatest common factor. Finally, the zero product property is used to find the solutions, resulting in two possible values for the variable.

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

• Divide both sides by a variable

• Multiply both sides by a constant

• Set one side of the equation to zero

• Add a constant to both sides

Why is it preferred to have a positive degree two term when solving a quadratic equation by factoring?

• It helps in identifying the roots

• It simplifies the equation

• It makes the equation easier to graph

• It is a requirement for all quadratic equations

What operation is performed to set the right side of the equation to zero?

• Subtract 2t squared and add 11t

• Add 2t squared and subtract 11t

• Divide by 2t squared and multiply by 11t

• Multiply by 2t squared and divide by 11t

What is the greatest common factor of 2t squared and 6t?

• 2

• 6t

• 2t

• t

What is the factored form of the left side of the equation?

• 2t(t - 3)

• 2t(t + 3)

• t(t - 3)

• t(t + 3)

What does the zero product property state?

• If a product is zero, one or both factors must be zero

• If a product is zero, the factors are equal

• If a product is zero, both factors must be non-zero

• If a product is zero, the factors are negative

How do you solve the equation 2t = 0?

• Divide both sides by 2

• Add 2 to both sides

• Multiply both sides by 2

• Subtract 2 from both sides

What is the solution to the equation t - 3 = 0?

• t = 3

• t = 0

• t = -3

• t = 6

What are the solutions to the given quadratic equation?

• t = 0 and t = -3

• t = 1 and t = 3

• t = 0 and t = 3

• t = 1 and t = -3

What is the purpose of factoring in solving quadratic equations?

• To find the roots of the equation

• To eliminate variables

• To convert to a linear equation

• To simplify the equation