Warm Up Compute the following by using long division. (You have 10 minutes and no calculators.) 1. 105/36 2. 210/ 82 3. 1956/ 15 4. 12350/ 27 5. 6239/ 18

Real Zeros of Polynomial Functions 2.4 Real Zeros of Polynomial Functions

Division Algorithm for Polynomials

Remainder Theorem

Example Using Polynomial Long Division f(x) = x2 – 2x + 3 ÷ x – 1

Examples

Example Using the Remainder Theorem

Example Use the Remainder Theorem to find the remainder when f(x) is divided by x – k. f(x) = x4 – 5; k = 1

Example Evaluate the function at x = 1 f(1) = (1)4 – 5 = -4

Example Using Synthetic Division

Example Using Synthetic Division

Rational Zeros Theorem

Example Finding the Real Zeros of a Polynomial Function

Example Finding the Real Zeros of a Polynomial Function

Example Finding the Real Zeros of a Polynomial Function

Example Finding the Real Zeros of a Polynomial Function

Example Finding the Real Zeros of a Polynomial Function

Example Finding the Real Zeros of a Polynomial Function