Solving Quadratic Equations and Factoring

The video tutorial explains how to solve quadratic equations by factoring. It begins with an introduction to the method, followed by a detailed explanation of the factoring process. The zero factor theorem is then applied to find solutions, which are verified by substituting them back into the original equation. The tutorial ensures understanding by checking the validity of the solutions.

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

• Add a constant to both sides.

• Divide the equation by the highest coefficient.

• Multiply all terms by zero.

• Move all terms to one side of the equation.

When factoring a trinomial with no common factors, what should you do first?

• Break down the quadratic term into two binomials.

• Add a constant to the trinomial.

• Multiply the trinomial by a factor of zero.

• Find the greatest common factor.

Which pair of numbers will multiply to 12 and add to 8?

• 7 and 1

• 5 and 3

• 6 and 2

• 3 and 4

What is the purpose of checking the multiplication and addition of terms in a factored expression?

• To ensure the equation is balanced.

• To find the greatest common factor.

• To verify the accuracy of the factoring.

• To simplify the equation further.

What does the zero factor theorem help you determine?

• The roots of the equation.

• The product of the constants.

• The highest power of x.

• The sum of the coefficients.

How do you solve the equation x + 6 = 0?

• Divide both sides by 6.

• Add 6 to both sides.

• Subtract 6 from both sides.

• Multiply both sides by 6.

What are the solutions to the equation x^2 + 8x + 12 = 0?

• x = 6 and x = 2

• x = -6 and x = -2

• x = 6 and x = -2

• x = -6 and x = 2

Why is it important to substitute the solutions back into the original equation?

• To eliminate any extraneous solutions.

• To simplify the equation further.

• To find additional solutions.

• To check if they satisfy the equation.

What is the result when substituting x = -6 into the original equation?

• The equation equals 12.

• The equation equals 0.

• The equation equals -12.

• The equation equals 6.

What is the result when substituting x = -2 into the original equation?

• The equation equals 2.

• The equation equals -4.

• The equation equals 0.

• The equation equals 4.