1,032 prompts matching "Testing whether a binary operation is closed on a given set"
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Common Mistakes: A sign error in the formula, and how to catch it
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Practice: Forming an equation from a given sum and product
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Common Mistakes: Roots that are reciprocals of one another
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Common Mistakes: A symmetric function needing the sum and product twice over
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Spot My Mistake: A pair with equal roots, meaning one solution only
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Show All Working: A simultaneous pair in which the second equation is a circle
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Common Mistakes: A word problem giving one linear and one quadratic equation
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Worked Example: The discriminant used as the test for intersection
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Common Mistakes: A line and a curve meeting once without the line being a tangent
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Common Mistakes: Multiplying one polynomial by another
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Learn: Setting out the division of a cubic by a linear expression
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Worked Example: The division algorithm for polynomials
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Practice: A division that leaves no remainder
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Show All Working: Synthetic division as a shorter route
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Common Mistakes: The degree of the quotient and of the remainder
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Final Revision: Writing the result of a polynomial division out in full
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Spot My Mistake: Finding two coefficients from two remainder conditions
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WAEC Prep: The remainder theorem checked against long division
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Common Mistakes: The remainder theorem applied to a quartic
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Common Mistakes: Using the factor theorem before dividing
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