Factoring and Solving Quadratic Equations

The video tutorial explains how to factor and solve quadratic equations with a leading coefficient of -1. It demonstrates the process of factoring out -1 to make the leading coefficient positive, allowing for standard factoring techniques. The tutorial provides examples, showing how to find factors that satisfy the equation and solve for x. It also covers the concept of double roots and multiplicity in solutions.

What is the first step in solving a quadratic equation with a leading coefficient of -1?

• Divide by -1

• Multiply by 2

• Factor out -1

• Add 1 to both sides

When factoring a quadratic equation, what should the leading coefficient be?

• Any positive number

• -1

• 1

• 0

Which pair of numbers multiplies to -18 and adds to -7?

• -2 and 9

• -3 and 6

• -6 and 3

• -9 and 2

What is the result of factoring the quadratic equation x^2 - 7x - 18?

• (x - 9)(x + 2)

• (x + 6)(x - 3)

• (x + 9)(x - 2)

• (x - 6)(x + 3)

After factoring, what is the next step to solve the equation?

• Multiply the factors

• Divide the factors

• Set each factor equal to zero

• Add the factors

What are the solutions to the equation (x - 9)(x + 2) = 0?

• x = -9 and x = -2

• x = 9 and x = -2

• x = 9 and x = 2

• x = -9 and x = 2

In the second example, what is the factored form of x^2 + 12x + 36?

• (x - 12)(x - 3)

• (x + 12)(x + 3)

• (x - 6)(x - 6)

• (x + 6)(x + 6)

What is the solution to the equation (x + 6)^2 = 0?

• x = 6

• x = -6

• x = 12

• x = 0

What does it mean when a solution has a multiplicity of 2?

• The solution is repeated twice

• The solution is incorrect

• The solution is doubled

• The solution is halved

What is another term for a solution with multiplicity of 2?

• Single root

• Double root

• Triple root

• Quadruple root