Polynomials - what you should know

Question 1

How to show that x-a is a factor of f(x)

Answer 1

To show x-a is a factor then use x=a in synthetic division and prove the remainder is 0, then state since the remainder is 0, x=a is a root and x-a is a factor.

Question 2

How to factorise a cubic

Answer 2

Using a factor of the coefficient without x then try each of these in synthetic division of the equation, then factorise the quadratic on the bottom row of the table.

Question 3

How to sketch the graph of a polynomial?

Answer 3

Find where the curve crosses the x axis - (y=0) and the y axis (x=0)
Differentiate and solve dy/dx =0 to find stationary points.
Use a nature table to determine nature.
Sketch out graph,