Understanding Rational Expressions and Factoring

The video tutorial explains how to find and simplify the function f/g of x, where f(x) and g(x) are given quadratic expressions. It covers the process of expressing f/g of x as a rational expression, factoring both the numerator and the denominator, and simplifying the expression while considering constraints to maintain the function's definition.

What is the expression for f(x) given in the video?

• x^2 + 15x - 8

• 2x^2 + 15x - 8

• x^2 + 10x + 16

• 2x^2 + 10x + 16

What is the expression for g(x) as described in the video?

• x^2 + 15x - 8

• 2x^2 + 15x - 8

• x^2 + 10x + 16

• 2x^2 + 10x + 16

What is the first step in simplifying the rational expression f(x)/g(x)?

• Subtract the expressions

• Factor the expressions

• Add the expressions

• Multiply the expressions

Which technique is used to factor the numerator 2x^2 + 15x - 8?

• Factoring by grouping

• Quadratic formula

• Completing the square

• Synthetic division

What are the two numbers used to split the middle term 15x in the numerator?

• 12 and 3

• 8 and 2

• 16 and -1

• 10 and 5

What is the factored form of the numerator 2x^2 + 15x - 8?

• (2x - 1)(x + 8)

• (x + 2)(x + 8)

• (2x + 1)(x - 8)

• (x - 2)(x - 8)

What are the two numbers that multiply to 16 and add to 10 for the denominator?

• 12 and 3

• 10 and 5

• 16 and -1

• 8 and 2

What is the factored form of the denominator x^2 + 10x + 16?

• (x + 2)(x + 8)

• (x + 4)(x + 4)

• (2x - 1)(x + 8)

• (x - 2)(x - 8)

What condition must be applied to the simplified expression to ensure it remains defined?

• x cannot be equal to -2

• x cannot be equal to 0

• x cannot be equal to -8

• x cannot be equal to 8

What is the final simplified form of the expression f(x)/g(x)?

• 2x + 1 over x - 8

• x - 2 over x + 8

• x + 2 over 2x - 1

• 2x - 1 over x + 2