College Algebra Review E.C

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What is the process of factoring a polynomial completely?

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Factoring a polynomial completely involves breaking it down into its simplest factors, which cannot be factored further. This often includes finding the greatest common factor (GCF) and applying techniques such as grouping, using special products, or the quadratic formula.

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What does it mean to expand a logarithm?

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Expanding a logarithm means rewriting it as a sum or difference of simpler logarithmic expressions using properties of logarithms, such as the product, quotient, and power rules.

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What is the process of condensing a logarithm?

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Condensing a logarithm involves combining multiple logarithmic expressions into a single logarithm using properties such as the product, quotient, and power rules.

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How do you factor out the common factor in an expression?

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To factor out the common factor, identify the greatest common factor (GCF) of the terms in the expression and divide each term by the GCF, then express the original expression as the product of the GCF and the remaining terms.

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What is the difference between factoring and expanding in algebra?

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Factoring is the process of breaking down an expression into its multiplicative components, while expanding is the process of multiplying out the factors to create a polynomial expression.

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What is the quadratic formula used for?

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

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What are the properties of logarithms?

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The main properties of logarithms include: 1) Product Rule: log_b(MN) = log_b(M) + log_b(N), 2) Quotient Rule: log_b(M/N) = log_b(M) - log_b(N), 3) Power Rule: log_b(M^p) = p * log_b(M).

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Example: 2x^3 - 4x^2 + 3x - 5.

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What does it mean for a polynomial to be factored completely?

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A polynomial is factored completely when it is expressed as a product of irreducible polynomials over the real numbers, meaning no further factoring is possible.

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What is the greatest common factor (GCF)?

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The greatest common factor (GCF) is the largest positive integer that divides all the terms of a polynomial without leaving a remainder.