Factoring and Simplifying Expressions

The video tutorial explains how to simplify rational expressions by factoring both numerators and denominators. It emphasizes the importance of factoring before simplification and provides two examples. The first example involves factoring a simple expression, while the second example deals with a more complex expression, highlighting the use of common factors. The tutorial concludes with helpful tips for simplifying rational expressions.

What is the first step in simplifying a rational expression?

• Multiplying the expressions

• Subtracting the denominators

• Factoring the numerators and denominators

• Adding the numerators

What is the greatest common factor in the expression Y^2 - 5Y?

• 5

• Y

• Y^2

• 5Y

How do you factor the expression Y^2 - 25?

• (Y + 5)(Y - 5)

• (Y - 5)(Y - 5)

• (Y - 5)(Y + 25)

• (Y + 5)(Y + 5)

Why can't you simplify Y/Y in the expression Y/(Y + 5)?

• Because of subtraction

• Because of addition

• Because of division

• Because of multiplication

What is the first step in factoring the more complex example?

• Factor out a 2

• Factor out a 4

• Factor out an X

• Factor out a 7

What common factor is found in the denominator of the second example?

• 2

• X

• 4

• 8

What are the factors of the trinomial X^2 - 3X + 2?

• (X + 2)(X - 1)

• (X - 2)(X + 1)

• (X - 1)(X - 2)

• (X + 1)(X + 2)

What is the purpose of factoring the denominator first in the second example?

• To simplify the numerator

• To add the terms

• To find a common factor

• To change the expression

What is the simplified form of the expression X(X - 2)/(4(X - 1))?

• X(X + 4)/(4(X + 1))

• X(X - 2)/(4(X + 1))

• X(X + 4)/(4(X - 1))

• X/4

What is a helpful strategy when simplifying complex rational expressions?

• Use the easier expressions to factor the more difficult ones

• Always start with the numerator

• Ignore the common factors

• Multiply the expressions first