Remainder theorem

Remainder theorem

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.

Lessons

\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})
  • 1.
    Understanding the remainder Theorem
    Prove the Remainder Theorem
    Remainder theorem

  • 2.
    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)
    a)
    Using synthetic division

    b)
    Using the remainder theorem


  • 3.
    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.