Simplifying Rational Expressions through Factoring

What does GCF stand for in the context of factoring expressions?

• General Calculus Function

• Greatest Common Factor

• Geometric Configuration Form

• Gradient Central Feature

How many terms does an expression need to have to use the product-sum table for factoring?

• Three

• Four

• Two

• One

What is the first step in simplifying a rational expression?

• Eliminate the common factors

• Factor the denominator

• Identify excluded values

• Factor the numerator

Which method is used to factor an expression with only two terms?

• Quadratic formula

• Binomial theorem

• Product-sum table

• GCF

What does the 'magic pair' refer to in the context of factoring by the product-sum table?

• The pair of terms that can be factored no further

• The initial pair of terms in the expression

• The pair of factors that sum up to the middle term

• The pair of highest common factors

What is the purpose of eliminating common factors in the context of simplifying expressions?

• To determine the GCF

• To expand the expression further

• To simplify the expression to its lowest terms

• To identify the product-sum table

After factoring and simplifying, what should you check for in the final expression?

• Magic pairs

• Numerical coefficients

• Additional factors

• Excluded values

What does setting a term equal to zero help to identify in the context of rational expressions?

• Common factors

• Excluded values

• Denominator factors

• Numerator factors

What are the excluded values in the final simplified expression of the tutorial?

• x = 9 and x = 3

• x = -9 and x = -3

• x = 9 and x = -3

• x = -9 and x = 3

Why is it important to understand excluded values in rational expressions?

• To make the expression easier to graph

• To avoid division by zero in the expression

• To ensure the expression is defined for all real numbers

• To simplify the expression correctly