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The Remainder Theorem

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

How to calculate a remainder using the Remainder Theorem?

What is the Remainder Theorem?
The Remainder Theorem states that:
If a polynomial f(x) is divided by (ax - b) then the remainder is given by f(b/a).

Maths : The Remainder Theorem : ExamSolutions
This tutorial shows you how to calculate a remainder using the remainder theorem
Example:
Find the remainder when 4x3 + 5x - 1 is divided by
(i) x - 2
(ii) 2x + 1
Maths : The Remainder Theorem (Example 1) : ExamSolutions
How to calculate a remainder using the remainder theorem?
Example:
Find the remainder when x3 - 4x2 + 2x - 3 is divided by x + 1



Maths : The Remainder Theorem (Example 2) : ExamSolutions
How to calculate a remainder using the remainder theorem?
Example:
Find the remainder when 4x4 - x2 - 8x + 6 is divided by 2x - 1
Maths : The Remainder Theorem (Example 3) : ExamSolutions
How to calculate constants in a polynomial using the remainder theorem?
Example:
When x3 + ax2 + bx - 1 is divided by x - 1 the remainder is 3 and when divided by x + 2 the remainder is -27. Find a and b.


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