Dividing Polynomials Intro - Chapter 4.1

Using Long Division Example 1: Dividing Polynomials DIVISOR DIVIDEND REMAINDER QUOTIENT

Example 2: Divide by Using Synthetic Division to Divide a Polynomial by a Divisor x – r r COEFFICIENTS OF THE DIVIDEND ** REMEMBER PLACE HOLDERS** COEFFICIENTS OF QUOTIENT REMAINDER

The final answer: It Means …

If is divided by then Division Algorithm: QUOTIENT DIVIDEND REMAINDER DIVISOR

 If the remainder is 0 then, the __________ and the ______________ are factors of dividend.  If a polynomial is divided by ___________, then the remainder is __________  A polynomial function has a linear factor x – a if and only if ___________  A polynomial of degree n has at most n distinct real ____________________. Things to Remember DIVISOR Example3: Find the remainder when is divided by x + 1 QUOTIENT ROOTS OR ZEROS

Let be a polynomial. If r is a real number that satisfies any of the following statements, then r satisfies any of the following statements:  r is a ________ of the function f  r is an ______________ of the graph of the function f  _____ is a solution, or root of the equation ________  ___________ is a factor of the polynomial f(x) ZERO

Asst. #48 Sect 4.1 pg #1-8, 9, 18, 22, 23, 28, 39, 45, 47, 50, 51, 57, 59, 61, 64, 69