Learn to solve a rational equation by factoring

The video tutorial covers the process of factoring equations, focusing on identifying common factors and understanding the Least Common Denominator (LCD). It explains how to apply the LCD to simplify equations and eliminate fractions. The tutorial also demonstrates distributing terms, simplifying equations, and factoring quadratic equations to find solutions. Finally, it emphasizes the importance of verifying solutions and identifying extraneous solutions.

What is the first step in simplifying an expression by factoring?

• Identify the LCD

• Apply the zero product property

• Find numbers that multiply to a specific product and add to a specific sum

• Use the quadratic formula

How do you determine the Least Common Denominator (LCD) in an expression?

• By subtracting the smallest denominator from the largest

• By dividing the largest denominator by the smallest

• By multiplying the common factors

• By adding all the denominators

What is the purpose of multiplying through by the LCD in an equation?

• To simplify the coefficients

• To eliminate fractions

• To increase the number of fractions

• To change the equation to a quadratic form

What is the result of distributing terms in a quadratic expression?

• A cubic equation

• A linear equation

• A quadratic equation

• A constant value

Which method is used to solve a quadratic equation after factoring?

• Zero product property

• Graphing

• Substitution

• Completing the square

What is an extraneous solution in the context of quadratic equations?

• A solution that is always positive

• A solution that is always negative

• A solution that does not satisfy the original equation

• A solution that satisfies the equation

Why is it important to check for extraneous solutions?

• To confirm the equation is quadratic

• To verify that solutions do not make the denominator zero

• To simplify the equation further

• To ensure all solutions are positive