Factoring Quadratic Equations Concepts

The video tutorial explains how to solve a quadratic equation by factoring. It begins with identifying the need to factor the equation when traditional algebraic methods are insufficient. The process involves finding two numbers whose sum and product match specific conditions, followed by factoring the expression using grouping. Finally, the tutorial demonstrates solving the factored equation to find the solutions, verifying them by substitution.

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

• Complete the square

• Use the quadratic formula

• Factor the expression

• Graph the equation

When looking for two numbers to factor a quadratic, what must their sum be in this example?

• Negative 2

• Negative 35

• Positive 35

• Positive 2

What is the product of the two numbers used to factor the quadratic equation in this example?

• -2

• 2

• -35

• 35

Which pair of numbers correctly factors the expression s^2 - 2s - 35?

• 1 and -35

• 5 and -7

• 2 and -17

• 7 and -5

What is the factored form of the expression s^2 - 2s - 35?

• (s - 5)(s + 7)

• (s + 5)(s - 7)

• (s - 5)(s - 7)

• (s + 5)(s + 7)

What property allows us to set each factor to zero to solve the equation?

• Zero Product Property

• Associative Property

• Commutative Property

• Distributive Property

If s + 5 = 0, what is the value of s?

• 7

• -5

• 5

• -7

If s - 7 = 0, what is the value of s?

• 5

• -5

• 7

• -7

What is the result of substituting s = -5 back into the original equation?

• 0

• 25

• -35

• 10

What is the result of substituting s = 7 back into the original equation?

• 49

• 14

• 0

• 35