Factoring Quadratic Equations and Verification

The video tutorial explains how to factor the quadratic equation x^2 - 16x + 63. It begins by setting up a skeleton equation and determining the signs based on the middle term. The instructor then finds factors of the last term, 63, that add up to the middle term, -16. The factors 7 and 9 are identified, and the equation is factored as (x - 7)(x - 9). The FOIL method is used to verify the correctness of the factors. Finally, the video demonstrates solving for X by setting each factor equal to zero, resulting in X values of 7 and 9. The instructor concludes by confirming that these solutions match those obtained using the quadratic formula.

What is the first step in factoring the equation x^2 - 16x + 63?

• Graph the equation.

• Use the quadratic formula.

• Set up a skeleton equation.

• Find the roots of the equation.

Why are two negative signs used in the skeleton equation for x^2 - 16x + 63?

• Because the middle term is negative.

• Because the first term is negative.

• Because the equation is quadratic.

• Because the last term is positive.

Which pair of numbers are the correct factors of 63 that add up to 16?

• 8 and 8

• 6 and 10

• 7 and 9

• 5 and 11

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

• FOIL method

• Completing the square

• Substitution method

• Graphing method

What is the result of combining -9x and -7x during verification?

• -18x

• -14x

• -16x

• -2x

What value of x satisfies the equation when x - 7 = 0?

• x = 9

• x = -7

• x = 7

• x = 0

What value of x satisfies the equation when x - 9 = 0?

• x = 7

• x = 0

• x = -9

• x = 9

What happens when you substitute x = 7 back into the original equation?

• The equation equals 7.

• The equation equals 9.

• The equation equals 0.

• The equation equals 1.

What does the quadratic formula confirm about the values of x?

• They are imaginary numbers.

• They are different from the factored values.

• They are the same as the factored values.

• They are incorrect.