Partial Fraction Decomposition Concepts

The video tutorial explains how to perform partial fraction decomposition on a rational expression. It begins by factoring the denominator using grouping, then sets up the partial fractions with linear and quadratic factors. The tutorial proceeds to clear fractions to form the principal equation and equates coefficients to create a system of equations. Finally, it solves the system using elimination and back substitution to find the constants A, B, and C, and substitutes these values to achieve the final partial fraction decomposition.

What is the first step in finding the partial fraction decomposition of a rational expression?

• Adding a constant to the expression

• Multiplying by the least common denominator

• Factoring the denominator

• Simplifying the numerator

When factoring by grouping, what is the common factor of the first two terms in the expression x^3 + 2x^2 + 9x + 18?

• x^2

• x + 2

• x

• 9

What are the types of factors in the denominator after factoring x^3 + 2x^2 + 9x + 18?

• Two quadratic factors

• A linear and a quadratic factor

• Two linear factors

• A cubic and a linear factor

What is the form of the numerator for the fraction with a quadratic denominator in partial fraction decomposition?

• A constant

• A linear expression

• A cubic expression

• A quadratic expression

What is the purpose of multiplying both sides of the equation by the least common denominator?

• To factor the expression

• To find the common factors

• To simplify the numerator

• To clear the fractions

What system of equations is formed by equating the coefficients in the partial fraction decomposition?

• A system with five equations

• A system with four equations

• A system with two equations

• A system with three equations

What method is used to eliminate B from the first two equations in the system?

• Substitution

• Factoring

• Graphing

• Elimination

After solving the system of equations, what is the value of A?

• 3

• 4

• 5

• 6

What is the final form of the partial fraction decomposition for the given expression?

• 6/(x+2) + (2x+5)/(x^2+9)

• 5/(x+2) + (3x+4)/(x^2+9)

• 3/(x+2) + (4x+5)/(x^2+9)

• 4/(x+2) + (3x+5)/(x^2+9)

What is the value of C in the partial fraction decomposition?

• 6

• 4

• 3

• 5