The Factor Theorem (Edexcel IGCSE Maths B): Revision Note

Factor Theorem

What is the factor theorem?

• The factor theorem is used to find the linear factors of a function

  • This is closely related to finding the roots (or solutions) of a function or equation

• For a function , the factor theorem tells us that

  • If  , then is a factor of

  •  If  is a factor of , then  

How do I use the factor theorem?

• Consider the  function where is a factor

  • Then by the factor theorem we know that

    • I.e.,  is a solution to the equation 

• Or consider the function where

  • Then by the factor theorem we know  that is a factor of

  • Therefore 

    • where is a function that is also a factor of

  • Hence  

    • I.e.  is the quotient when  is divided by 

    • And the remainder is equal to zero

• If the linear factor has a coefficient of x (other than 1) you must first factorise out the coefficient

  • For the linear factor  

    • 

    •