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Questions and Answers
What is the result of the synthetic division of (4x² + x - 3) by (x - 3)?
What is the correct remainder when dividing (x² + x³ - 3x² - 4x - 4) by (x + 3)?
When (3x² + 4x - x² - 2x³ - 4) is divided by (x + 2), what is the quotient?
What do you obtain as the quotient when dividing (2x⁵ - 2x³ + 4x² - 3) by (x + 1)?
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What is the other term used for the number sign #?
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Study Notes
Polynomial Division Overview
- Synthetic division is a streamlined method for dividing polynomials, suitable for linear divisors.
- Identify the dividend (numerator) and divisor (denominator) in the division process.
Examples of Synthetic Division Problems
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C) (4x² + x - 3) ÷ (x - 3)
- Determine quotient Q(x) and remainder r(x) through synthetic division.
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E) (x² + x³ - 3x² - 4x - 4) ÷ (x + 3)
- Rearranging terms may help in better organizing the division process.
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H) (3x² + 4x - x² - 2x³ - 4) ÷ (x + 2)
- Combine like terms and then apply synthetic division.
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O) (2x⁵ - 2x³ + 4x² - 3) ÷ (x + 1)
- Focus on the highest degree terms for initial setup in synthetic division.
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P) (-x⁴ + 2x⁵ - 2x - 3x² + 1) ÷ (x - 2)
- Arranging terms in descending order can simplify the division process.
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T) (-25 - 4x⁴ - 3x² + 4x) ÷ (x - 4)
- Watch for signs to ensure accurate calculation when using synthetic division.
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R) (2x³ + 5x² - 4x - 5) ÷ (2x + 1)
- Pay attention to coefficients and adjust accordingly in synthetic division.
Additional Note
- The other term for the number sign (#) is "hash" or "pound."
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Description
This quiz challenges you to perform synthetic division on various polynomials. For each polynomial division, identify the quotient Q(x) and the remainder r(x). Complete your solution and match the remainder to the given decoder.
