Factoring Quadratic Equations and Solutions

The video tutorial explains how to factor and solve quadratic equations using the difference of squares method. It emphasizes the importance of factoring out the greatest common factor first. Two examples are provided: one involving the equation 48X^2 - 75 and another with 2X^2 - 32. The tutorial demonstrates how to factor these equations and solve for X, highlighting the use of the zero product property to find solutions.

What is the first step in factoring a quadratic equation in the form of A^2 - B^2?

• Add the terms together

• Multiply the terms

• Factor out the greatest common factor

• Divide the terms by 2

When factoring 48x^2 - 75, what is the greatest common factor?

• 2

• 3

• 4

• 5

After factoring out the greatest common factor, what form does the equation 48x^2 - 75 take?

• 3(x^2 - 25)

• 3(16x^2 - 25)

• 3(16x^2 + 25)

• 3(x^2 + 25)

What is the zero product property used for in solving quadratic equations?

• To add solutions

• To find the greatest common factor

• To set each factor equal to zero

• To multiply solutions

What are the solutions to the equation 4x + 5 = 0?

• x = 5/4

• x = -5/4

• x = 4/5

• x = -4/5

In the second example, what is the first step to solve the equation?

• Multiply both sides by 2

• Add 32 to both sides

• Divide both sides by 2

• Subtract 32 from both sides

What is the greatest common factor in the equation 2x^2 - 32?

• 16

• 8

• 2

• 4

What are the solutions to the equation x^2 - 16 = 0?

• x = 4 and x = -4

• x = 16 and x = -16

• x = 8 and x = -8

• x = 2 and x = -2

How can the solutions x = 4 and x = -4 be expressed in a shorter form?

• x = ±2

• x = ±16

• x = ±8

• x = ±4

What is the most important step to remember when factoring quadratic equations?

• Always add the terms first

• Always divide the terms first

• Always multiply the terms first

• Always factor out the greatest common factor