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# Remainder theorem

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• 4.4 Remainder Theorem Objectives In this lesson you will learn how to find the remainder when a polynomial is divided by a linear divisor by an elegant method using the remainder theorem .
• Exercise 4.4, Page 88, Question 1 (a)
• Exercise 4.4, Page 88, Question 3
• Exercise 4.4, Page 89, Question 8
• ### Remainder theorem

1. 1. Polynomials and Partial Fractions Objectives In this lesson, you will learn how to find the remainder when a polynomial is divided by a linear divisor, by an elegant method - using the remainder theorem . 4.4 Remainder Theorem
2. 2. In the previous lesson, we saw that: We will generalise this result as the remainder theorem. Polynomials and Partial Fractions Then: And if x = 1:
3. 3. If a polynomial P( x ) is divided by a linear divisor ( x – a ), the remainder is P( a ). The remainder theorem is a much simpler and more elegant way of finding the remainder compared to long division. Polynomials and Partial Fractions Then: And if x = a : Let Q( x ) be the quotient and R be the remainder.
4. 4. Let x = – 1. The remainder is 6. Find the remainder when . Polynomials and Partial Fractions By the remainder theorem, when P( x ) is divided by x + 1, Substitute for x in P( x ). Example
5. 5. Let x = – 2 a. Polynomials and Partial Fractions Find the possible values of a. Substitute for x in P( x ). By the remainder theorem, when P( x ) is divided by x + 2 a, R = 32. There are two possible values of a . Example
6. 6. Let x = 1. Polynomials and Partial Fractions Substitute for x in P( x ). By the remainder theorem, when P( x ) is divided by x – 1, Equating remainders Shown By the remainder theorem, when P( x ) is divided by x + 1, Substitute for x in P( x ). Let x = – 1. Example .