Download presentation

Presentation is loading. Please wait.

Published byShavonne Harrington Modified over 8 years ago

1
9.4 Polynomial Division ©2006 by R. Villar All Rights Reserved

2
Warm-up Factor each: 1. 27x 3 – 64 2. 2x 3 – 3x 2 + 4x – 6 (3x – 4)(9x 2 + 12x + 16)(2x 3 – 3x 2 ) + (4x – 6) x 2 (2x – 3) + 2(2x – 3) (2x – 3)(x 2 + 2)

3
Polynomial Division, Factors, and Remainders In this section, we will look at two methods to divide polynomials: long division (similar to arithmetic long division) synthetic division (a quicker, short-hand method) Let’s take a look at long division of polynomials...

4
Example: Divide (2x 2 + 3x – 4) ÷ (x – 2) (x – 2) 2x 2 + 3x – 4 Rewrite in long division form... divisor dividend Think, how many times does x go into 2x 2 ? 2x Multiply by the divisor. 2x 2 – 4x Subtract. 7x – 4 Think, how many times does x go into 7x ? + 7 7x – 14 10 remainder 2x + 7 + 10 x – 2 divisor Write the result like this...

5
Example: Divide (p 3 – 6) ÷ (p – 1) (p – 1) p 3 + 0p 2 + 0p – 6 Be sure to add “place-holders” for missing terms... p2p2 p 3 – p 2 p 2 + 0p + p p 2 – p p – 6 p 2 + p + 1 – 5 p – 1 + 1 p – 1 –5 Let’s look at an abbreviated form of long division, called synthetic division...

6
Synthetic division can be used when the divisor is in the form (x – k). Example: Use synthetic division for the following (2x 3 – 7x 2 – 8x + 16) ÷ (x – 4) First, write down the coefficients in descending order, and k of the divisor in the form x – k : 4 2 –7 –8 16 k 2 Bring down the first coefficient. 8 Multiply this by k 1 Add the column. 4 –4 –16 0 These are the coefficients of the quotient (and the remainder) 2x 2 + x – 4 Repeat the process.

7
Example: Divide (5x 3 + x 2 – 7) ÷ (x + 1) –1 5 1 0 –7 Notice that k is –1 since synthetic division works for divisors in the form (x – k). place-holder 5x 2 – 4x + 4 – 11 x + 1 5 –5 –4 4 4 –11

8
You Try: Divide (2x 4 + x 3 – 2x 2 + 9x + 5) ÷ (2x+ 1) (2x + 1) 2x 4 + x 3 – 2x 2 + 9x + 5 2x 4 + x 3 – 2x 2 + 9x x3x3 –2x 2 – x 10x + 5 x 3 – x + 5 – x+ 5 10x + 5 0

9
You Try: Divide (3x 4 + 12x 3 – 5x 2 – 18x + 8) ÷ (x + 4) –4 3 12 –5 –18 8 3x 3 – 5x – 2 3 –12 0 0 –5 20 2 –8 0

10
Assignment p. 484: 7 – 29 odd, skip 13

Similar presentations

© 2023 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