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Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths.

**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

H**ow 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) = 2x^{3} - 3x^{2} - 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

x^{3} – 2x^{2} – 4x + 8

is divided by

(i) x – 3,

(ii) x + 2.

(b) Hence, or otherwise, find all the solutions to the equation

x^{3} – 2x^{2} – 4x + 8 = 0

**A-Level Maths Edexcel C2 January 2007 Q5(a) : ExamSolutions**

f(x) = x^{3} + 4x^{2} + 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

x^{3} + 4x^{2} + 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

More Lessons for A Level Maths

Math Worksheets

Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths.

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

H

f(x) = 2x

(a) Use the factor theorem to show that (x + 4) is a factor of f(x).

(b) Factorise f(x) completely

This question is on the factor theorem and solving a cubic equation.

(a) Find the remainder when

x

is divided by

(i) x – 3,

(ii) x + 2.

(b) Hence, or otherwise, find all the solutions to the equation

x

f(x) = x

(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

x

Worked solution to the above Core 2 question on the factor theorem

Worked solution to the above Core 2 question on the factor theorem

Factorise cubic equation

Worked solution to the above Core 2 question on the factor theorem

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