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The remainder theorem worksheets Grades 10–11

Find the remainder of P(x) ÷ (x − c) by working out P(c).

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Free · Worked example · 14 problems · Answer key · US Letter

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How to do it

P(c) is the remainder when P(x) is divided by x − c.

P(x)=x2−6x+2;P(4)=−6P(x) = x^{2} - 6x + 2;\quad P(4) = -6
The remainder is −6, so P(4)=−6.\text{The remainder is }-6,\ \text{so }P(4) = -6.the remainder theorem
P(4)=(4)2−6(4)+2=−6P(4) = (4)^{2} - 6(4) + 2 = -6check by putting it in

Example problems

  1. P(x)=2x2−6x−5;P(−3)=P(x) = 2x^{2} - 6x - 5;\quad P(-3) =
  2. P(x)=x3+5x2+2x+6;P(3)=P(x) = x^{3} + 5x^{2} + 2x + 6;\quad P(3) =
  3. P(x)=x2+5x−5;P(−2)=P(x) = x^{2} + 5x - 5;\quad P(-2) =
  4. P(x)=3x3+4x2−x−6;P(4)=P(x) = 3x^{3} + 4x^{2} - x - 6;\quad P(4) =

Quadratic and polynomial functions

  1. Vertex form of a quadratic
  2. Finding the vertex from standard form
  3. The discriminant
  4. Quadratic equations with complex roots
  5. Polynomial long division
  6. Synthetic division
  7. The remainder theorem
  8. The factor theorem
  9. The rational root theorem