College Algebra Review

Front

What is the process of factoring a polynomial?

Back

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

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What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form by combining like terms, reducing fractions, or eliminating unnecessary parentheses. For example, 2x + 3x simplifies to 5x.

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What is the difference between an expression and an equation?

Back

An expression is a combination of numbers, variables, and operations without an equality sign, while an equation states that two expressions are equal, indicated by an equality sign (e.g., 2x + 3 = 7).

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, indicating the power to which a base must be raised to produce a given number. For example, log_b(a) = c means b^c = a.

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How do you condense logarithmic expressions?

Back

To condense logarithmic expressions, use the properties of logarithms, such as log_b(m) + log_b(n) = log_b(m*n) and log_b(m) - log_b(n) = log_b(m/n).

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What is the quadratic formula?

Back

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

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What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 3x^2 are not.

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What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parentheses.

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How do you solve for a variable in an equation?

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To solve for a variable, isolate it on one side of the equation using inverse operations, such as addition, subtraction, multiplication, or division.

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What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables raised to non-negative integer powers and coefficients, such as 4x^3 - 2x^2 + x - 5.