M - Pure 1 - 7) Algebraic methods

Question 1

Rules of the factor theorem

Answer 1

• If f(p) = 0, then (x – p) is a factor of f(x)
• If (x – p) is a factor of f(x), then f(p) = 0

Question 2

Method to factorise a cubic function using the factor theorem

Answer 2

1. Substitute values into the function to find a value of p where f(p) = 0
2. Divide the function by (x – p) using algebraic long division
3. Write f(x) = (x – p)(ax² + bx + c)
4. Try factorise the quadratic factor
5. Write f(x) as a product of three linear factors