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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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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