Solving Quadratic Equations and Factors

This video tutorial demonstrates how to solve a quadratic equation using the factor by grouping method. It begins by setting the equation to zero, identifying coefficients, and finding factors. The tutorial then explains how to rewrite the BX term, group terms, and factor out common factors. Finally, it solves the equation using the zero product property and verifies the solutions through substitution.

What is the first step in solving a quadratic equation using factor by grouping?

• Divide the equation by the highest coefficient

• Multiply all terms by a constant

• Add a constant to both sides

• Set the equation to zero

What are the coefficients 'a', 'b', and 'c' in the equation 12x^2 + 20x + 3 = 0?

• a = 12, b = 20, c = 3

• a = 20, b = 12, c = 3

• a = 3, b = 12, c = 20

• a = 12, b = 3, c = 20

Which pair of numbers are factors of 36 that add up to 20?

• 2 and 18

• 4 and 9

• 3 and 12

• 6 and 6

How is the term 20x rewritten using the factors 2 and 18?

• Neither A nor B

• 18x + 2x

• Both A and B

• 2x + 18x

What is the greatest common factor of the first group 12x^2 + 2x?

• 6x

• 2x

• 12x

• x

What is the common binomial factor in the expression after grouping?

• 6x + 1

• 2x + 3

• 12x + 3

• 18x + 3

What is the solution for x when 6x + 1 = 0?

• x = -1/6

• x = 1/6

• x = -6

• x = 6

What is the solution for x when 2x + 3 = 0?

• x = 2/3

• x = -3/2

• x = 3/2

• x = -2/3

Which property is used to solve the equation by setting each factor to zero?

• Commutative Property

• Zero Product Property

• Associative Property

• Distributive Property

How can you verify the solutions of the quadratic equation?

• Ensure the solutions are integers

• Check if the solutions are positive

• Substitute the solutions back into the original equation

• Verify the solutions are less than 10