Factoring and Solving Equations

This video tutorial demonstrates how to factor the quadratic equation x^2 - 7x + 12 = 0. It begins by setting up a skeleton equation and identifying the factors of 12 that sum to 7. The factorization is verified using the FOIL method. Finally, the video shows how to solve for x and verify the solutions by substituting them back into the original equation.

What is the first step in factoring the equation x^2 - 7x + 12 = 0?

• Add the coefficients

• Set up a skeleton equation

• Multiply the terms

• Divide by x

When adding signs to the skeleton equation, what sign is placed in the middle?

• Positive

• Negative

• None

• Zero

Which pair of factors of 12 adds up to 7?

• 5 and 2

• 1 and 12

• 2 and 6

• 3 and 4

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

• Graphing

• Substitution

• FOIL method

• Completing the square

What is the result of multiplying the first terms in the FOIL method for this equation?

• 12

• x

• x^2

• 7x

How do you solve for x in the equation (x - 3)(x - 4) = 0?

• Divide by 2

• Multiply the factors

• Add the factors

• Set each factor equal to zero

What value of x satisfies the equation x - 3 = 0?

• x = 3

• x = -3

• x = 0

• x = 4

What value of x satisfies the equation x - 4 = 0?

• x = 3

• x = 0

• x = -4

• x = 4

What is the result when substituting x = 3 back into the original equation?

• 0

• 7

• 3

• 12

What is the result when substituting x = 4 back into the original equation?

• 16

• 4

• 0

• 8