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Factor Theorem Exam Questions

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What is the Factor Theorem?
For a polynomial f(x)
(1) if f(a) = 0 for some number a then (x - a) is a factor of f(x)
(2) if (x - a) is a factor then f(a) = 0

How to use the Factor Theorem to factorise cubic equations?

The Factor Theorem - Edexcel Maths A-Level A-Level Maths Edexcel C2 June 2008 Q1a ExamSolutions
f(x) = 2x3 - 3x2 - 39x + 20
(a) Use the factor theorem to show that (x + 4) is a factor of f(x).
(b) Factorise f(x) completely A-Level Maths Edexcel C2 January 2008 Q1b ExamSolutions
This question is on the factor theorem and solving a cubic equation.
(a) Find the remainder when
x3 – 2x2 – 4x + 8
is divided by
(i) x – 3,
(ii) x + 2.
(b) Hence, or otherwise, find all the solutions to the equation
x3 – 2x2 – 4x + 8 = 0



A-Level Maths Edexcel C2 January 2007 Q5(a) : ExamSolutions
f(x) = x3 + 4x2 + x - 6
(a) Use the factor theorem to show that (x + 2) is a factor of f(x).
(b) Factorise f(x) completely
(c) Write down all the solutions to the equation
x3 + 4x2 + x - 6 = 0
Worked solution to the above Core 2 question on the factor theorem A-Level Maths Edexcel C2 January 2007 Q5(b) : ExamSolutions
Worked solution to the above Core 2 question on the factor theorem
Factorise cubic equation A-Level Maths Edexcel C2 January 2007 Q5(c) : ExamSolutions
Worked solution to the above Core 2 question on the factor theorem

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