Simplifying Rational expressions

The video tutorial covers the process of simplifying trigonometric expressions by factoring. It begins with an introduction to the importance of factoring and the challenges posed by addition and subtraction in expressions. The instructor then explains the grouping technique, a method used to factor expressions with four terms. A detailed, step-by-step application of this technique is demonstrated, showing how to factor out common terms and simplify the expression. The tutorial concludes with a discussion on the limitations of further simplification and the final expression.

Why can't the properties of exponents be applied directly to simplify trigonometric expressions?

• Because they involve complex numbers.

• Because they are already in their simplest form.

• Because they are separated by addition and subtraction.

• Because they are separated by multiplication.

What is the first step in the grouping technique for factoring?

• Multiply all terms together.

• Combine all terms into one.

• Break up the terms into pairs.

• Add a constant to each term.

When using the grouping technique, what should you factor out from each pair of terms?

• The least common multiple.

• The smallest number.

• The largest number.

• The greatest common factor.

In the expression X^2 - 8X + 15, what two numbers multiply to 15 and add to -8?

• -5 and -3

• 5 and 3

• -8 and 1

• 7 and -2

Why can't X^2 - 3 and X - 3 be simplified further by division?

• They are already in simplest form.

• They are separated by multiplication.

• They are not the same terms.

• They are not separated by addition.