Solving Quadratic Equations and Factoring

The video tutorial explains how to solve quadratic equations by factoring. It covers several examples, including solving equations with perfect square trinomials and using the difference of squares method. The tutorial emphasizes the importance of setting the equation to zero and finding factors that satisfy the equation.

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

• Divide both sides by x

• Set the equation to zero

• Multiply both sides by a constant

• Add a constant to both sides

In the equation x^2 + 4x = 21, what should you do after setting it to zero?

• Divide by 4

• Add 21 to both sides

• Find two numbers that multiply to -21 and add to 4

• Factor out x

What are the solutions to the equation x^2 + 4x - 21 = 0?

• x = 7 and x = -3

• x = -7 and x = 3

• x = -7 and x = -3

• x = 7 and x = 3

What is a perfect square trinomial?

• A trinomial with no real solutions

• A trinomial that can be factored into two identical binomials

• A trinomial that cannot be factored

• A trinomial with a negative constant

How do you recognize a difference of squares?

• When the equation has a constant term

• When the equation is in the form a^2 - b^2

• When the equation has a term with x

• When the equation is linear

What are the solutions to the equation x^2 - 64 = 0?

• x = 8 and x = -8

• x = 64 and x = -64

• x = 0 and x = 64

• x = 8 and x = 64

What is the solution to the equation x^2 - 24x + 144 = 0?

• x = -24

• x = 24

• x = -12

• x = 12

In the equation 4x^2 - 25 = 0, what is the value of a in the difference of squares?

• 2x

• 5

• x

• 25

What is the solution to the equation 4x^2 - 25 = 0?

• x = 5 and x = -5

• x = 5/2 and x = -5/2

• x = 2 and x = -2

• x = 25 and x = -25

What is the general form of a difference of squares?

• a^2 - 2ab + b^2

• a^2 + b^2

• a^2 - b^2

• a^2 + 2ab + b^2