Remainder theorem

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Examples
Lessons
  1. Understanding the remainder Theorem
    Prove the Remainder Theorem
    Remainder theorem
    1. Finding the Remainder Using Synthetic Division and the Remainder Theorem
      Find the remainder when (4x3−7x+10)\left( {4{x^3} - 7x + 10} \right) is divided by (2x−5)\left( {2x - 5} \right)
      1. Using synthetic division
      2. Using the remainder theorem
    2. When (8x3+ax2+bx−1)\left( {8{x^3} + a{x^2} + bx - 1} \right) is divided by:
      i) (2x−5)\left( {2x - 5} \right), the remainder is 5454
      ii) (x+1)\left( {x + 1} \right), the remainder is −30 - 30
      Find the values of aa and bb.
      Topic Notes
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      You may want to refresh your memory on polynomial long division and synthetic division to better understand this lesson. The remainder theorem simply states that if a polynomial f(x) is divided by a linear expression x-r, the value of f(r) is equal to the remainder.
      ⋅\cdot When a polynomial, P(x)P(x), is divided by (x−a)(x-a): Remainder =P(a)=P(a)
      ⋅\cdot When a polynomial, P(x)P(x), is divided by (ax−b)(ax-b): Remainder =P(ba)=P(\frac{b}{a})
      Basic Concepts
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      Related Concepts
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