Advanced Algebra: Benchmark 2 Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication. Example: 3x^2 + 2x - 5.

Front

Define the degree of a polynomial.

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

What is the difference between a monomial and a binomial?

Back

A monomial is a polynomial with one term (e.g., 5x), while a binomial has two terms (e.g., 3x + 2).

Front

Explain the concept of factoring a polynomial.

Back

Factoring a polynomial involves expressing it as a product of its factors. For example, x^2 - 5x + 6 can be factored into (x - 2)(x - 3).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Define a rational function.

Back

A rational function is a function that can be expressed as the ratio of two polynomials. Example: f(x) = (2x + 3) / (x^2 - 1).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

Explain the concept of asymptotes in rational functions.

Back

Asymptotes are lines that a graph approaches but never touches. Vertical asymptotes occur where the denominator is zero, while horizontal asymptotes describe the behavior as x approaches infinity.

Front

What is the process of completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Front

Define exponential growth and decay.

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when it decreases at a rate proportional to its current value.