Download presentation

Presentation is loading. Please wait.

Published byAshlyn Cobb Modified over 8 years ago

1
6.4 Multiplying/Dividing Polynomials 1/10/2014

2
How do you multiply 1256 by 13?

3
Example 1 Multiply Polynomials Vertically Find the product. () x 2x 2 4x4x7 – + () 2x – SOLUTION Line up like terms vertically. Then multiply as shown below. x 2x 2 4x4x7 – + 2x – × 2x 22x 2 8x8x+14 –– Multiply by 2. x 2x 2 4x4x7 – + – x 3x 3 7x7x+ – 4x 24x 2 Multiply by x. x 2x 2 4x4x7 – + x 3x 3 15x+ – 2x 22x 2 +14 Combine like terms.

4
Example 2 Multiply Polynomials Horizontally Find the product. () 4+3x3x () 5x 25x 2 x6 – + a. 4+3x3x () 5x 25x 2 x6 – + () 5x 25x 2 x6 – + = Use distributive property. SOLUTION () 4+3x3x () 5x 25x 2 x6 – + a. + 15x 3 18x – +20x 2 4x4x24 – + = 3x 23x 2 Use distributive property. 15x 3 + 24 – = 20x 2 3x 23x 2 + 18x4x4x – + Group like terms. 15x 3 14x – + = 23x 2 24 – Combine like terms.

5
Example 2 Multiply Polynomials Horizontally () 2x – () x 2x 2 2x2x3 – + = b. () 2x – () 1x – () 3x + + x 3x 3 3x3x – +2x 22x 2 4x4x6 – = 2x 22x 2 – Use distributive property. x 3x 3 + 6 = 2x 22x 2 2x 22x 2 3x3x4x4x – – – + Group like terms. + x 3x 3 7x7x – 6 = Combine like terms. 2x – () x 2x 2 2x2x3 – + = () x 2x 2 2x2x3 – + Multiply any 2 binomials Multiply by the 3 rd binomial

6
Checkpoint Multiply Polynomials Find the product. Use either a horizontal or vertical format. 1. () 1+x () x 2x 2 x2++ 2. () 2x 22x 2 x4 – + () 3x – ANSWER 2x 22x 2 3x3x2x 3x 3 +++ 7x 27x 2 7x7x122x 32x 3 + ––

7
Checkpoint Multiply Polynomials Find the product. Use either a horizontal or vertical format. 3. () 1+2x2x () 3x 23x 2 x1 – + ANSWER 5x 25x 2 x16x 36x 3 + –– x 2x 2 10x8x 3x 3 + – + () 1x – 4. () 4x + () 2x –

8
Checkpoint Use Special Product Patterns Find the product. () 7z – () 7z + 5. ANSWER z 2z 2 49 – 6. ()2)2 23y3y + 12y9y 29y 2 4++ ANSWER 64x 3 + – 12x48x 2 – 1 ANSWER 7. – ()3)3 14x4x

9
Homework: Worksheet 6.4

10
6.4 Multiplying/Dividing Polynomials….cont’d. 1/29/2014

11
Example 4 Use Long Division Find the quotient 985 23. ÷ Divide 98 by 23. 985 23 -92 Subtract the product. 4 () 23 = 92 65 Bring down 5. Divide 65 by 23. 19 Remainder ANSWER The result is written as. 23 19 42 -46 Subtract the product. 2 () 23 = 46 42

12
Example 5 Use Polynomial Long Division Find the quotient. () 4x + x 3x 3 + – 6x6x 3x 23x 2 – 4 () ÷ Write division in the same format you use to divide whole numbers. x 3x 3 +4x 24x 2 Subtract the product. () 4x + x 2x 2 = x 3x 3 4x 24x 2 + – 6x6xx 2x 2 – Bring down - 6x. Divide –x 2 by x – 4x4xx 2x 2 – Subtract the product. () 4x + x = x 2x 2 4x4x ––– – 2x2x – 4 Bring down - 4. Divide -2x by x 4 Remainder x 3x 3 + – 6x6x3x 23x 2 – 4x+4 x 3x 3 ÷x = x 2x 2 ANSWER The result is written as. x 2x 2 –– x2 x+4 4 + – 2x2x – 8 Subtract the product () 4x + 2 = 2x2x8 –––. x2x2 -x -2 - +

13
Example 5 Use Polynomial Long Division CHECKYou can check the result of a division problem by multiplying the divisor by the quotient and adding the remainder. The result should be the dividend (what’s inside ). +4x 2x 2 –– x2 () x+4 () = x+4 () x 2x 2 – xx+4 () – 2x+4 () +4 = x 3x 3 –– 4x4x+44x 24x 2 x 2x 2 + – 2x2x – 8 = x 3x 3 – 6x6x3x 23x 2 + – 4

14
Synthetic division: Is a method of dividing polynomials by an expression of the form x - k

15
Example 1 Using Synthetic division x – (-4) in x – k form -4Coefficients of powers of x 1 3 -6 -4 k 1 -4 4 multiply -2 8 4 add coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend. ANSWER x 2x 2 –– x2 x+4 4 + remainder

16
Example 2 Using Synthetic division 3 Coefficients of powers of x 2 -7 0 6 -14 k 2 6 -3 multiply -3 -9 -23 add remainder -3 -9 ANSWER

17
Checkpoint Find the quotient. 5x5x4x 34x 3 + () +1x ( +1 ) ÷ ANSWER 4x4x4x24x2 + – 9+ x+1 8 –

18
Example 3 Use Polynomial Long Division Can’t use synthetic division because it isn’t being divided by x-k - + remainder

19
Example 3 Use Polynomial Long Division Can’t use synthetic division because it isn’t being divided by x-k - + - remainder

20
Homework: WS: Dividing Polynomials

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