Factoring and Simplifying Rational Expressions

This video tutorial demonstrates how to multiply rational expressions with quadratic trinomials in both the numerators and denominators. The process involves factoring each part and canceling common factors to simplify the expression. The instructor provides a step-by-step guide, emphasizing the importance of identifying factors that will cancel out, and offers tips for factoring complex trinomials using trial and error.

What is the main idea when multiplying rational expressions with quadratic trinomials?

• Simplifying by combining like terms

• Multiplying and dividing terms

• Factoring and canceling common factors

• Adding and subtracting terms

What are the two numbers that multiply to -8 and add up to -2 in the denominator of the first expression?

• 2 and -4

• -2 and 4

• 4 and -2

• -4 and 2

What is the factored form of x^2 - 2x - 8?

• (x - 2)(x + 4)

• (x - 4)(x + 2)

• (x + 2)(x + 4)

• (x - 4)(x - 2)

Which two numbers multiply to -4 and add up to -3 in the numerator of the second expression?

• -1 and 4

• 4 and -1

• -4 and 1

• -2 and 2

What is the factored form of x^2 - 3x - 4?

• (x - 4)(x + 1)

• (x - 1)(x + 4)

• (x + 1)(x - 4)

• (x + 4)(x - 1)

What is the factored form of x^2 + 3x + 2?

• (x + 1)(x + 2)

• (x - 1)(x + 2)

• (x + 1)(x - 2)

• (x - 1)(x - 2)

What is the factored form of 3x^2 + 7x + 2?

• (3x + 1)(x + 2)

• (3x + 2)(x + 1)

• (3x - 1)(x + 2)

• (3x + 1)(x - 2)

Which terms cancel out in the simplified form of the rational expressions?

• x + 1 and x - 2

• x + 1 and x + 2

• x - 4 and x + 2

• x + 2 and x - 4

What is left in the numerator after canceling common factors?

• x + 2

• 3x + 1

• x - 4

• x + 1

What is left in the denominator after canceling common factors?

• x + 1

• x - 4

• x + 2

• 3x + 1