Rational Expressions and Factoring

The video tutorial explains how to simplify a rational expression by factoring both the numerator and the denominator. It also covers how to determine the domain of the expression by identifying values that make the denominator zero. The process involves factoring by grouping and simplifying the expression by canceling common factors. The domain is all real numbers except those that make the denominator zero.

What is the first step in simplifying a rational expression?

• Subtracting the denominator from the numerator

• Multiplying the numerator by the denominator

• Factoring both the numerator and denominator

• Adding the numerator and denominator

Which method is used to factor the numerator 2x^2 + 13x + 20?

• Factoring by substitution

• Factoring by grouping

• Factoring by elimination

• Factoring by division

What are the two numbers that multiply to 40 and add up to 13 in the numerator?

• 4 and 9

• 6 and 7

• 3 and 10

• 5 and 8

What is the factored form of the numerator 2x^2 + 13x + 20?

• (x + 4)(x + 5)

• (2x + 4)(x + 5)

• (x + 4)(2x + 5)

• (2x + 5)(x + 6)

What are the two numbers that multiply to 60 and add up to 17 in the denominator?

• 5 and 12

• 7 and 10

• 6 and 11

• 8 and 9

What is the factored form of the denominator 2x^2 + 17x + 30?

• (x + 5)(x + 6)

• (2x + 5)(x + 6)

• (x + 4)(2x + 5)

• (2x + 4)(x + 5)

Which x-values make the denominator of the rational expression undefined?

• x = -4 and x = -5

• x = -6 and x = -5/2

• x = -3 and x = -2

• x = -7 and x = -1

What is the domain of the rational expression?

• All real numbers except x = -7 and x = -1

• All real numbers except x = -3 and x = -2

• All real numbers except x = -4 and x = -5

• All real numbers except x = -6 and x = -5/2

What is the simplified form of the rational expression?

• x + 4 over x + 5

• x + 4 over x + 6

• x + 6 over x + 4

• x + 5 over x + 6

Why can the factor 2x + 5 be canceled from the rational expression?

• Because it equals zero

• Because it is only in the denominator

• Because it is only in the numerator

• Because it is a common factor in both the numerator and denominator