Factoring Quadratic Equations and Solutions

In this video, Dr. B demonstrates how to solve the quadratic equation x^2 + 6x + 9 = 0 by factoring. The process begins with setting up the equation skeleton and adding signs. Next, the factors of the last term, 9, that add up to the middle term, 6, are identified. The factors are verified using the FOIL method. Finally, the solution for x is found and checked to ensure accuracy.

What is the first step in solving the equation x^2 + 6x + 9 = 0 by factoring?

• Use the quadratic formula

• Graph the equation

• Complete the square

• Set up the skeleton for factoring

When setting up the equation for factoring, what signs are used in the binomials?

• One positive, one negative

• Both positive

• No signs are needed

• Both negative

Which pair of numbers are factors of 9 that add up to 6?

• 1 and 9

• 3 and 3

• 5 and 1

• 2 and 4

What method is used to verify the factorization of the equation?

• Completing the square

• Graphing

• FOIL method

• Substitution

What is the result of the first step in the FOIL method for the equation (x + 3)(x + 3)?

• x^2

• 3x

• 9

• 6x

What value of x makes the equation (x + 3)(x + 3) = 0 true?

• x = 3

• x = -3

• x = 0

• x = 6

How can you verify that x = -3 is a solution to the equation?

• By substituting x = -3 into the original equation

• By completing the square

• By using the quadratic formula

• By graphing the equation

What is the sum of the numbers when x = -3 is substituted into the equation x^2 + 6x + 9?

• 3

• 0

• 9

• 6

What is the purpose of factoring the equation x^2 + 6x + 9 = 0?

• To rewrite the equation in standard form

• To calculate the y-intercept

• To determine the x-intercepts

• To find the vertex of the parabola

What is the final step after factoring the equation to find the solution?

• Complete the square

• Use the quadratic formula

• Verify the solution by substitution

• Graph the equation