792 prompts matching "Structured question: binomial expansion with a negative term"
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Explain Back: Finding a coefficient when the remainder is given
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Show All Working: A remainder of nought, and what it means
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Common Mistakes: The remainder theorem applied to a quartic
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Worked Example: Testing a list of candidates to find a factor
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Practice: Showing that x plus 3 is a factor of a given polynomial
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Explain Back: Finding a coefficient so that a stated expression is a factor
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Show All Working: What the factor theorem says about the roots
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Common Mistakes: Using the factor theorem before dividing
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Worked Example: Factorising a cubic into a linear and a quadratic factor
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Practice: Factorising a quartic as the product of two quadratics
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Common Mistakes: Factorising fully, and knowing when to stop
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Worked Example: How many roots a cubic equation has
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Show All Working: Solving a cubic that must first be rearranged
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Common Mistakes: A cubic equation arising from a volume problem
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Worked Example: Sentences that are not propositions
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Practice: The conjunction of two propositions
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Explain Back: The disjunction of two propositions
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Show All Working: Translating an English sentence into logical symbols
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Common Mistakes: Translating a symbolic statement back into English
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Worked Example: Conjunction in a three-variable truth table
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