What is polynomial factorisation?

• Factorising a polynomial combines the?factor theorem?with the method of?polynomial division
• The goal is to break down a polynomial as far as possible into a product of?linear factors

How do I factorise a polynomial?

• At A level you will usually be asked to factorise a?cubic?– i.e. a polynomial where the highest power of?x?is 3

• To factorise a cubic polynomial?f(x)?follow the following steps:

• Step 1. Find a value?p?that makes?f(p) =?0

• Step 2. Use polynomial division to divide?f(x)?by?(x?-?p)

• Step 3. Use the result of your division to write

f(x) = (x?-?p) (ax2?+?bx?+?c)

• Step 4. If the quadratic?(ax2?+?bx?+?c)?is factorisable, factorise it and write?f(x)?as a product of three linear factors (if the quadratic is not factorisable, then your result from Step 3 is the final factorisation)