Remainder theorem

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  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 (4x37x+10)\left( {4{x^3} - 7x + 10} \right) is divided by (2x5)\left( {2x - 5} \right)
      1. Using synthetic division
      2. Using the remainder theorem
    2. When (8x3+ax2+bx1)\left( {8{x^3} + a{x^2} + bx - 1} \right) is divided by:
      i) (2x5)\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
      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 (xa)(x-a): Remainder =P(a)=P(a)
      \cdot When a polynomial, P(x)P(x), is divided by (axb)(ax-b): Remainder =P(ba)=P(\frac{b}{a})