# 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

The following diagram shows the Factor Theorem and the Remainder Theorem. Scroll down the page for more examples and solutions. 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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