1,045 prompts matching "Structured question: use binomial expansion to approximate a value"
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Worked Example: The identity linking alpha squared plus beta squared to the sum and product
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Final Revision: Using a symmetric function to find an unknown coefficient
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Worked Example: Substituting into the quadratic and tidying up
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Practice: The condition for the line to be a tangent
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Explain Back: The condition for the line never to meet the curve
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Show All Working: The point of contact when a line touches a curve
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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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Spot My Mistake: The factor theorem applied to a quartic
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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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Quiz: Factorising a polynomial by grouping terms
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Practice: Factorising a quartic as the product of two quadratics
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Explain Back: A polynomial with a repeated linear factor
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Spot My Mistake: Factorising the sum of two cubes
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Show All Working: Factorising a polynomial with fractional roots
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Common Mistakes: Factorising fully, and knowing when to stop
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