Download presentation

Presentation is loading. Please wait.

3
Section 7.3 Products and Factors of Polynomials

4
Factoring the Sum and Difference of Two Cubes

5
Factor Theorem (x-r) is a factor of the polynomial expression that defines the function P if and only if r is a solution of P(x) = 0, that is, if and only if P(r) = 0. In other words: – Set x-r = 0 – Solve for x. x = r – Plug this r in for every x in the original polynomial – Simplify – If you get 0 then (x – r) IS a factor of the polynomial

9
Let’s look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient of 1. #1#2

10
Step #1: Write the terms of the polynomial so the degrees are in descending order.

11
Step #2: Write the constant a of the divisor x- a to the left and write down the coefficients.

12
Step #3: Bring down the first coefficient, 5.

13
Step #5: After multiplying in the diagonals, add the column. Add the column

14
Multiply the diagonals, add the columns. Add 15*3 = 45

15
Step #7: Repeat the same procedure as step #6. Add Columns

16
The quotient is: Remember to place the remainder over the divisor.

17
Step #8: Write the quotient. The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend.

23
Divide a polynomial by a monomial.

25
Divide the following numbers. Check

26
Divide the following numbers (Long Division) Remainder

27
Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

28
Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

29
Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

30
Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

31
Dividing a polynomial by a polynomial (Long Division) NOW YOU WRITE THIS ONE

32
Dividing a polynomial by a polynomial (Long Division)

33
NOW YOU WRITE THIS ONE

34
Dividing a polynomial by a polynomial (Long Division)

38
Homework Problems 1. 2. 3. 4.

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google