Test #11 - Algebra 3

Front

Define partial fraction decomposition.

Back

Partial fraction decomposition is a technique used to express a rational function as the sum of simpler fractions, making it easier to integrate or analyze.

Front

What is the formula for factoring a difference of cubes?

Back

Front

Factor the expression: 27x³ - 64.

Back

(3x - 4)(9x² + 12x + 16).

Front

What are the steps to factor a polynomial?

Back

1. Look for a common factor. 2. Use special factoring formulas (difference of squares, perfect square trinomials, etc.). 3. Factor by grouping if applicable. 4. Check for irreducibility.

Front

Define the term 'leading coefficient' in a polynomial.

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What is the significance of the Rational Root Theorem?

Back

The Rational Root Theorem provides a way to find possible rational roots of a polynomial equation, which can help in factoring the polynomial.

Front

Factor the expression: 49m³q² - 35mq² - 42m³q⁴p².

Back

7mq²(7m² - 5 - 6m²p²q²).

Front

What is the process to find values of A and B in algebraic equations?

Back

To find values of A and B, set up a system of equations based on the given conditions and solve using substitution or elimination.

Front

Explain the concept of a polynomial's degree.

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

What is the purpose of factoring in algebra?

Back

Factoring simplifies expressions, makes solving equations easier, and helps in finding roots of polynomials.