The Factor Theorem: Suppose p is a nonzero polynomial. . Solution. 1. The Remainder Theorem states p(-2) is the remainder when p(x) is divided by x - (-2). CHAPTER 18 POLYNOMIAL DIVISION AND THE FACTOR AND. REMAINDER THEOREMS .. + x – 6 and hence solve the cubic equation x. 3. + 4x. 2. – x – 6 = . The Remainder and Factor Theorems; Synthetic Division Example 3: Check your answer for the division problems in Example 2. The Division Algorithm: If.
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. Using the above Theorem and your results from question 1 which of the given binomials are Remainder Theorem and Factor Theorem (Answers). 1. Exercises: 1. can see, division doesn't always produce a polynomial answer – sometimes there's Use the remainder theorem to find the remainder of the following divisions and then Section 4 The factor theorem and roots of polynomials.
- The Remainder Theorem and the Factor Theorem. Example. The multiplicity of a solution is. Example. When f(x) is divided by x − r, the remainder is. 3 is a factor of the polynomial, 3 is also a solution to the equation x2. 2x – 15 By the factor theorem, 2 is a zero of the function if and only if the remainder is. writing the answer in ascending powers of x. 2. 3. 4. 3 7. 3 a) Use the factor theorem to show that ()2 x + . the remainder is exactly the same as when (). f x is.