Factoring Quadratic Equations and Functions

The video tutorial explains how to factor the quadratic equation x^2 + 4x - 32. It begins by setting up a skeleton equation and adding appropriate signs. The tutorial then identifies factors of -32 that sum to 4, and verifies the factorization using the FOIL method. Finally, it solves for x values that satisfy the equation, confirming the results with the quadratic formula.

What is the first step in factoring the equation x^2 + 4x - 32?

• Find the greatest common factor.

• Graph the equation.

• Use the quadratic formula.

• Set up a skeleton equation.

When the last term of a quadratic equation is negative, what signs should be used in the skeleton equation?

• No signs are needed.

• One positive and one negative sign.

• Two negative signs.

• Two positive signs.

Which pair of factors of -32 adds up to the middle term 4 in the equation x^2 + 4x - 32?

• 4 and 8

• 2 and 16

• 1 and 32

• 8 and -4

What method is used to verify the factorization of the equation x^2 + 4x - 32?

• Completing the square

• Substitution method

• Graphing method

• FOIL method

What is the result of combining the terms after using the FOIL method on the factors of x^2 + 4x - 32?

• x^2 + 8x - 32

• x^2 - 4x + 32

• x^2 + 4x - 32

• x^2 - 8x + 32

What value of x makes the equation (x + 8)(x - 4) equal to zero?

• x = -8

• x = 8

• x = -4

• x = 4

What is the other value of x that makes the equation (x + 8)(x - 4) equal to zero?

• x = -4

• x = -8

• x = 8

• x = 4

If you substitute x = -8 into the equation x^2 + 4x - 32, what is the result?

• The equation equals 0.

• The equation equals 32.

• The equation equals 8.

• The equation equals -8.

If you substitute x = 4 into the equation x^2 + 4x - 32, what is the result?

• The equation equals 0.

• The equation equals -8.

• The equation equals 8.

• The equation equals 32.

What alternative method can be used to verify the solutions of the equation x^2 + 4x - 32?

• Synthetic division

• Quadratic formula

• Graphing method

• Completing the square