3 2 The Factor Theorem and The Remainder Theorem 265 3 2 1 Exercises In Exercises 1 - 6, use polynomial long division to perform the indicated division
In this section, we will learn to use the remainder and factor theorems to factorise and to solve polynomials that are of degree higher than 2 Before doing so,
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
Target: On completion of this worksheet you should be able to use the remainder and factor theorems to find factors of polynomials
4 2 8 - The Factor Theorem 4 2 - Algebra - Solving Equations The Factor Theorem (x - a) is a factor of the polynomial f (x) if and only if f (a) = 0
(Hint: Refer to Example 6 ) Page 3 Page 3 (Section 5 1) Remainder Theorem Factor Theorem
Use the Factor Theorem to determine if the binomials given are factors of f(x) Use the binomials that are factors to write a factored form of f(x) f(x) = x*
After studying the slides, you should attempt the Consolidation Questions #uniofsurrey 2 Page 3 2 3 Learning checklist #
Note: Checking this using long division will give the same remainder of ?2 see Example 5 from Section 2) 4 Page 5 Exercises: 1 Use the remainder theorem
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
(Hint: Refer to Example 6 ) Page 3 Page 3 (Section 5 1) Remainder Theorem Factor Theorem
The Factor Theorem and Algebraic Division Exercise 1: The Factor Theorem 1 a The cubic function p is defined by p( ) = 3 − 2 2 − 5 + 6
a) Use the factor theorem to find two linear factors of ( ) f x b) Hence show that the equation ( ) 0 f x = has exactly two real roots