HA2 1st Semester Final Review

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What is the Least Common Denominator (LCD) and how is it used in solving equations?

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The Least Common Denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions. It is used to eliminate fractions in equations by multiplying both sides by the LCD.

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How do you subtract complex numbers?

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To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (10 - 6i) - (2 + 3i) = (10 - 2) + (-6i - 3i) = 8 - 9i.

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What is synthetic division and when is it used?

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Synthetic division is a simplified form of polynomial division, used when dividing a polynomial by a linear factor of the form (x - c). It is faster and requires less writing than long division.

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Perform synthetic division on: (2x^3 - 5x - 7) ÷ (x - 2)

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The result is: 2x^2 + 4x + 3 - \frac{1}{x - 2}.

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to whole number exponents and coefficients. Example: 2x^3 - 5x + 7.

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Define a rational expression.

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What is the difference between a rational and an irrational number?

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Explain the concept of imaginary numbers.

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