Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Factor theorem
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. 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. 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. 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. 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. 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 .
Editor's Notes
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 .
