Factoring and Solving Quadratic Equations

The video tutorial explains how to solve a quadratic equation by factoring. It begins with setting up the equation by subtracting terms to form a standard quadratic equation. The instructor then demonstrates factoring by identifying two numbers that multiply to the product of the first and last coefficients and add to the middle coefficient. The process involves listing factor pairs and selecting the correct pair. The equation is then factored by grouping, and each factor is set to zero to solve for x, resulting in two solutions.

What is the first step in solving the given quadratic equation?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 6 from both sides

• Add 6 to both sides

What is the resulting equation after subtracting 6 from both sides?

• 2x^2 - x + 6 = 0

• 2x^2 + x - 6 = 0

• 2x^2 - x - 6 = 0

• 2x^2 + x + 6 = 0

What is the product of the first and last numbers in the quadratic equation?

• 6

• 12

• -6

• -12

Which pair of factors of -12 adds up to the middle term (1)?

• -1 and 12

• -4 and 3

• -2 and 6

• -3 and 4

How is the middle term split using the identified factors?

• 3x - 4x

• 4x - 3x

• -4x + 3x

• -3x + 4x

What is the GCF of the first group in the equation?

• x

• 2

• 2x

• 3

What is the GCF of the second group in the equation?

• 2x

• x

• 3

• 2

What is the factored form of the quadratic equation?

• (2x + 3)(x - 2)

• (2x - 3)(x + 2)

• (2x - 2)(x + 3)

• (2x + 2)(x - 3)

What is the value of x when solving 2x - 3 = 0?

• 3/2

• -2/3

• 2/3

• -3/2

What is the value of x when solving x + 2 = 0?

• 2

• -1

• -2

• 1