Unit 2: Functions
Topic 2.12: Factor & remainder (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 2.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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x⁴ − 1 is divisible by (x − 1) with remainder:
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For 4x² − 12x + 9 = 0, the product of the roots is:
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Write down the roots of and their multiplicities.
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The roots of 3x² + 5x − 2 = 0 are α and β. Find α + β and αβ.
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If 4 + i is a root of a real quartic, another root must be:
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Write down the remainder when is divided by .
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The remainder when x³ + x − 5 is divided by (x − 2) is:
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The roots of x² − 9x + 20 = 0 have sum and product:
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A cubic with positive leading coefficient and three real roots:
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Find the remainder when 2x³ + 3x² − x + 4 is divided by (x + 1).
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If x³ − 7x + 6 has (x − 1) as a factor, the other quadratic factor is:
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Factorise x³ − 3x² − x + 3 fully.
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Given that (x − 2) is a factor of x³ + kx² − 4x − 12, find k.
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The cubic x³ + ax² + bx + 6 has roots 1, 2 and 3. Find a and b.
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P(x) = x³ + 2x² − x − 2. Find the roots and the y-intercept, then describe the sketch.
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