1,019 prompts matching "A set closed under one operation but not another"
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Common Mistakes: Proving that a quadratic expression is positive for every real x
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Final Revision: Solving a disguised quadratic by substitution
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Quiz: Finding alpha cubed plus beta cubed
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Spot My Mistake: Forming an equation whose roots are alpha squared and beta squared
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WAEC Prep: Forming an equation whose roots are alpha over beta and beta over alpha
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Show All Working: Finding a coefficient given a stated relation between the roots
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Common Mistakes: Symmetric functions when the three roots of a cubic are involved
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Final Revision: Checking a symmetric-function answer by solving the equation outright
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Quiz: The factor theorem, and testing whether x minus a is a factor
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Spot My Mistake: The factor theorem for a divisor of the form ax minus b
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WAEC Prep: Sketching a cubic from its factorised form
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Show All Working: Solving a cubic equation by factorisation
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Common Mistakes: Adding, subtracting and multiplying two polynomials
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Final Revision: The zeros of a polynomial and where its graph cuts the x-axis
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Quiz: The product of the roots of a cubic
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Spot My Mistake: The relations between roots and coefficients for a quartic
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Show All Working: Three roots in arithmetic progression in a cubic
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Common Mistakes: Three roots in geometric progression in a cubic
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Final Revision: Checking that the roots found satisfy the original equation
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Quiz: Solving a quadratic inequality using a sign table
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