Polynomials

• Polynominal division 


  Calculate $\frac{x^3-x^2-11x-4\ }{x-4}$

  divide $x^3$ by $x$

  Mutiply $x^2$ by $\left(x-4\right)$

  subtract to get the remainder, then divide $3x^2$by $x$

  mutiply $3x$ by $\left(x-4\right)$

  subtract to get remainder, then divide $x$ by $x$

  Mutiply by $\left(x-4\right)$

  Subtract - this time there is no remiander

  
• sketching polynomials functions 


  To sketch the graph of a polynomials function :

  • classify the order of the polynomial and whether its positive or negative to deduce basic shape
  • set x=0 to find y-intercept
  • write the expression in factorised form
  • identify x interecepts
  • Decide how the curve meets the x-axis at each intercept
  • use all this information to draw a smooth curve