Simplifying Rational Expressions and Factoring

This video tutorial covers simplifying rational expressions, focusing on techniques like factoring and canceling terms. It begins with an introduction to rational expressions and moves on to simplifying monomials and binomials. Various factoring methods, such as GCF, trinomial factoring, and difference of squares, are discussed. The tutorial also addresses special cases and the commutative property, providing examples to illustrate these concepts.

What is the primary goal when simplifying rational expressions?

• To cancel like terms after factoring

• To add the expressions

• To multiply the expressions

• To divide the expressions

When simplifying a fraction like 15x^2/5x, what is the simplified form?

• 15x

• x

• 5x

• 3x

Which method is used to factor expressions with four terms?

• GCF

• Difference of squares

• Trinomial factoring

• Grouping

What is the result of factoring the expression x^2 - 64?

• (x + 2)(x - 2)

• (x + 16)(x - 16)

• (x + 4)(x - 4)

• (x + 8)(x - 8)

In the expression 2x^2 + 7x + 10, what are the factors?

• (x + 7)(x + 10)

• (2x + 2)(x + 5)

• (x + 5)(x + 2)

• (2x + 5)(x + 2)

What is the simplified form of the expression a^2 - 25?

• (a + 5)(a - 5)

• (a + 3)(a - 3)

• (a + 10)(a - 10)

• (a + 2)(a - 2)

What is the result of factoring 4x^2 + 8x + 3x + 6 using grouping?

• (x + 2)(4x^2 + 6)

• (x + 2)(4x^2 + 3)

• (x + 3)(4x^2 + 2)

• (x + 6)(4x^2 + 3)

How do you handle subtraction in expressions like 2 - x and x - 2?

• Multiply them

• Factor out a negative one to make them equivalent

• They are the same and can be canceled directly

• Add them together

What is the commutative property in relation to addition?

• a + b = b + a

• a - b = b - a

• a * b = b - a

• a / b = b / a

What is the simplified form of the expression 3 - x over x - 3?

• 0

• -1

• 1

• 3