Solving Quadratic Equations by Factoring

This video tutorial covers solving quadratic equations using the factoring technique. It introduces the zero product property, which is essential for solving these equations. The tutorial provides a detailed example, demonstrating how to break down a quadratic equation into factors and solve for the variable. The process involves identifying factors that multiply to a specific value and using the zero product property to find solutions.

What is the primary technique discussed for solving quadratic equations in the video?

• Using the quadratic formula

• Graphing

• Completing the square

• Factoring

What property is essential for solving quadratic equations by factoring?

• Commutative property

• Distributive property

• Associative property

• Zero product property

What must be true for the zero product property to be applied?

• The equation must be linear

• The equation must have no real solutions

• The equation must equal zero

• The equation must equal one

What does the zero product property allow us to do with a factored quadratic equation?

• Divide each side by the leading coefficient

• Multiply the factors

• Set each factor equal to zero

• Combine like terms

What values are considered when factoring the quadratic equation in the example?

• Factors of -18 that add up to -7

• Factors of 18 that subtract to 7

• Factors of -7 that add up to -18

• Factors of 7 that subtract to 18

How do you verify the correct factorization of a quadratic expression?

• By using the quadratic formula

• By graphing the equation

• By applying the zero product property

• By foiling the factors and comparing to the original equation

What is the first step in solving quadratic equations by factoring as discussed in the video?

• Factor the quadratic expression

• Set the equation to zero

• Identify the coefficients

• Isolate the x variable

Which of the following is a correct factor pair used in the example for -18?

• All of the above

• 3 and 6

• 2 and 9

• 1 and 18

What are the solutions to the quadratic equation after applying the zero product property?

• x = 9 and x = 2

• x = -9 and x = 2

• x = -9 and x = -2

• x = 9 and x = -2

After factoring, what is the next step to find the solutions of the quadratic equation?

• Combine like terms

• Apply the quadratic formula

• Graph the equation

• Set each factor equal to zero and solve