Polynomials

Question 1

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

Answer 1

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

Question 2

How do you factorise a cubic?

Answer 2

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

Question 3

How do you sketch the graph of a polynomial?

Answer 3

Find where the curve crosses the x-axis (y = 0) and the x-axis (x = 0)

Differentiate and solve dy over dx to find the stationary points

Use a nature table to determine nature

Sketch the graph