3 2 The Factor Theorem and The Remainder Theorem Suppose we wish to find the zeros of f(x) = x3 + 4x2 - 5x - 14 Setting f(x) = 0 results in the
To find the value of k, rewrite the divisor in the form x k Because x 2 x (2) , k 2 x2 x 3
where k is a constant (a) Write down the value of f (k) (1) When f (x) is divided by (x – 2) the remainder is 4 (b) Find the value of k
24 fév 2015 · Useful in determining factors of a polynomial The Factor Theorem A special case of the remainder theorem The factor theorem states: • When
An important consequence of the Factor Theorem is that finding the zeros of a polynomial is really the same thing as factoring it into linear factors
How can you use your answer in part K to determine the factors of a polynomial? This can be generalized into a theorem, known as the remainder theorem
Find the remainder when Using the above Theorem and your results from question 1 which of the given binomials are the remainder is 26, find k
Factor Theorem: A polynomial f (x) has a factor x - k if and only if f (k) = 0 Example #1: f(x) = x²+x-2 Given that x-1 is a factor, find the other factor
Solution To find the zeros, solve x(20 - 2x)(16 - 2x) = 0 By the Zero-Product Theorem, at least one of these factors must equal zero
Theorem, Factor Theorem, and Rational Zeros Theorem; and find upper and lower bounds for zeros of polynomials 1 1 Lesson objectives is r = f(k)
This means that we no longer need to write the quotient polynomial down, nor the x in the divisor, to determine our answer -2 x3+4x2- 5x -14 2x2 12x 14 x3 6x2
(b) Find the value of k (2) Page 2 C2 Algebra: Remainder Factor Theorems
(c) find the remainder when f(x) is divided by (2x – 3) la (a) Use the factor theorem to show that (x +4) is a factor of 2x + x2 - 25x+12 f(x) = (3x - 2)(x -- k) - 8
Example 1: Use long division to find the quotient and the remainder: use synthetic division and the Remainder Theorem to find the indicated function If the same factor (x – r) occurs k times, then the zero r is called a zero with multiplicity k
1 3 Division of Polynomials; Remainder and Factor Theorems Objectives • Perform long Find the quotient and remainder when the polynomial x 2 + x − 6 is For what value(s) of k do you get a remainder of 15 when you divide kx 3 + 2x