Polynomials

Question 1

How do you show that x-a is a factor of f(x)?

Answer 1

Use synthetic division to show that the remainder is zero or show that f(a) = 0

Question 2

How do you factorise a cubic?

Answer 2

First find a linear factor, using synthetic division the factorise the quadratic from the bottom row of the table

Question 3

How do you sketch the graph of a polynomial?

Answer 3

1. Find where the curve crosses the
   x-axis (y=0) and the y-axis (x=0)
2. Differentiate and solve f’ (x) = 0 to find stationary points
3. Use nature table to determine nature
4. Sketch graph