The answer comes from our old friend, polynomial division Dividing The Remainder Theorem: Suppose p is a polynomial of degree at least 1
Example 1 Find the remainder when ( ) = 3 + ?4 ?1 is divided by ( ? 2) Solution By the Remainder Theorem, the remainder is (2)
If f(x) is a polynomial and f(a) = 0, then (x–a) is a factor of f(x) Proof of the factor theorem Let's start with an example Consider 4 8 5
The aim of this unit is to assist you in consolidating and developing your knowledge and skills in working with the factor and remainder theorems It
Target: On completion of this worksheet you should be able to use the remainder and factor theorems to find factors of polynomials
Example 3: Check your answer for the division problems in Example 2 The Division Algorithm: If f(x) and d(x) are polynomials where d(x)? 0 and degree d
(x - a) is a factor of the polynomial f (x) if and only if f (a) = 0 Answer: 4 2 - Algebra - Solving Equations 4 2 8 - The Factor Theorem
2 Remainder and Factor Theorems Interactive Mathematics Factor theorem state with proof examples and solutions factorise the Polynomials Maths Mutt
writing the answer in ascending powers of x 2 3 5 1 x x x + + + Question 8 (**+) a) Use the factor theorem to show that ( )5 x ? is a factor of
Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled You must show sufficient working to make your methods
The answer comes from our old friend, polynomial division The Remainder Theorem: Suppose p is a polynomial of degree at least 1 In Exercises 21 - 30, determine p(c) using the Remainder Theorem for the given polynomial func-
writing the answer in ascending powers of x 2 3 5 1 x x x + + + Question 8 (** +) a) Use the factor theorem to show that ( )5 x − is a factor of 3 19 30 x x −
and factor theorems to find factors of polynomials A26 This gives an easy way of finding the remainder when a polynomial is divided by (x – a) Examples 1
polynomial division Example 1 Divide 14 5 4 2 3