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Grade 12 · Precalculus

Polynomial & rational functions

288 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Let f(x)=x4−5x3−4x2+7x+9f(x) = x^{4} - 5x^{3} - 4x^{2} + 7x + 9. According to Descartes' rule of signs, what is the maximum possible number of positive real zeros of ff?

  2. Warm-up

    Let f(x)=x4+5x3−5x2−9x−9f(x) = x^{4} + 5x^{3} - 5x^{2} - 9x - 9. According to Descartes' rule of signs, what is the maximum possible number of positive real zeros of ff?

  3. Warm-up

    Let f(x)=x4−8x3+2x2−3x+4f(x) = x^{4} - 8x^{3} + 2x^{2} - 3x + 4. According to Descartes' rule of signs, what is the maximum possible number of positive real zeros of ff?

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