Download presentation

Presentation is loading. Please wait.

Published byRoss Newman Modified over 8 years ago

1
Do Now Pass out calculators. Write down the weeks assignments. Pick up a worksheet from the back and wait for instructions.

2
Objective: To divide polynomials.

3
SOLUTION Divide a polynomial by a monomial EXAMPLE 1 Divide 4x 3 + 8x 2 + 10x by 2x. Method 1 : Write the division as a fraction. Write as fraction. Divide each term by 2x. = 2x 2 + 4x + 5 8x28x2 4x34x3 2x2x 2x2x 10x 2x2x ++= Simplify. (4x 3 + 8x 2 + 10x) 2x 4x 3 + 8x 2 +10x 2x2x =

4
Divide a polynomial by a monomial EXAMPLE 1 CHECK 2x(2x 2 + 4x + 5) = 4x 3 + 8x 2 + 10x ? 2x(2x 2 ) + 2x(4x) + 2x(5) = 4x 3 + 8x 2 + 10x ? 4x 3 2x = ? Think 8x 2 2x = ? Think 10x 2x = ? Think + 4x + 5 ANSWER (4x 3 + 8x 2 + 10x) 2x = 2x 2 + 4x + 5 2x 4x 3 + 8x 2 + 10x ) 2x22x2 4x 3 + 8x 2 + 10x = 4x 3 + 8x 2 + 10x

5
GUIDED PRACTICE for Example 1 (6x 3 + 3x 2 –12x) 3x1. 2x 2 + x – 4 ANSWER (12y 4 – 16y 3 + 20y 2 ) 4y2. ANSWER 3y 3 – 4y 2 + 5y

6
SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x – 1. Multiply x and x – 1. x x – 1x 2 + 2x – 3 x 2 – x 3x3x Subtract x 2 – x from x 2 + 2x. Think : x 2 x = ?

7
EXAMPLE 2 Divide a polynomial by a binomial Bring down –3. Then divide the first term of 3x – 3 by the first term of x – 1. + 3 3x – 3 0 Multiply 3 and x – 1. Subtract 3x – 3 from 3x – 3. STEP 2 Think : 3x x = ? ANSWER (x 2 + 2x – 3) (x – 1) = x + 3 x – 1x 2 + 2x – 3 x 2 – x 3x – 3 x

8
EXAMPLE 3 Divide a polynomial by a binomial Divide 2x 2 + 11x – 9 by 2x – 3. x 2x 2 –3x 2x – 3 2x 2 + 11x – 9 14x – 9 12 Multiply x and 2x – 3. Subtract 2x 2 – 3x. Bring down – 9. Multiply 7 and 2x – 3. Subtract 14x – 21. ANSWER (2x 2 + 11x – 9) (2x – 3) = x + 7 + 12 2x – 3 14x – 21 + 7

9
GUIDED PRACTICE for Examples 2 and 3 3. Divide: (a 2 + 3a – 4) (a + 1) a + 2 + ANSWER – 6 a + 1 4. Divide: (9b 2 + 6b + 8) (3b – 4) ANSWER 3b + 6 + 32 3b – 4

10
EXAMPLE 4 Rewrite polynomials Divide 5y + y 2 + 4 by 2 + y. Rewrite polynomials. Multiply y and y + 2. y 2 + 2y Subtract y 2 + 2y. Bring down 4. 3y + 4 Multiply 3 and y + 2. 3y + 6 Subtract 3y + 6. – 2 y + 2 y 2 + 5y + 4 y ANSWER (5y + y 2 + 4) (2 + y) = y + 3 + y + 2 – 2 + 3

11
EXAMPLE 5 Insert missing terms Divide 13 + 4m 2 by – 1 + 2m. Rewrite polynomials, Insert missing term. 2m2m 2m – 1 4m 2 + 0m + 13 Multiply 2m and 2m – 1. 4m 2 – 2m Subtract 4m 2 – 2m. Bring down 13. 2m + 13 Multiply 1 and 2m – 1. 2m – 1 Subtract 2m – 1. 14 ANSWER (13 + 4m 2 ) (– 1 + 2m) = 2m + 1 + 2m – 1 14 + 1

12
GUIDED PRACTICE for Examples 4, 5, and 6 5. Divide: (8m – 7 + 4m 2 ) (5 + 2m) ANSWER 2m – 1+ 2m + 5 – 2 6. Divide: (n 2 – 6) (– 3 + n) n + 3 + ANSWER n – 3 3

13
Exit Ticket: 1. Divide 6x 3 – 12x 2 + 9x by 3x. 1. Divide x 2 + x – 6 by x + 3. 1. Divide 3x 2 + 17x + 13 by 3x + 2. 1. Divide -12 + 4y 2 by -1 + 2y.

Similar presentations

© 2024 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