Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.
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Transcript of Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.
![Page 1: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/1.jpg)
Chapter 6 – Polynomials and Polynomial Functions
6.4 – Multiplying and Dividing Polynomials
![Page 2: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/2.jpg)
6.4 – Multiplying and Dividing PolynomialsToday we will be learning how to:
Multiply and divide polynomials
![Page 3: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/3.jpg)
6.4 – Multiplying and Dividing Polynomials
To multiply two polynomials, you multiply each term of the first polynomial by each term of the second polynomial.
You can use a vertical or a horizontal format.
![Page 4: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/4.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 1 - verticallyFind the product of (3x2 + 3x + 5)(2x + 3)
![Page 5: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/5.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 2 - horizontallyFind the product of
(x – 5)(x2 – 2x + 3)
(x + 3)(x – 4)(x + 5)
![Page 6: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/6.jpg)
6.4 – Multiplying and Dividing Polynomials
Special ProductsSum and Difference
(a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 16
Square of a binomial (a + b)2 = a2 + 2ab + b2
(x + 3)2 = x2 + 6x + 9 (a – b)2 = a2 – 2ab + b2
(3x – 4)2 = 9x2 – 24x + 16
![Page 7: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/7.jpg)
6.4 – Multiplying and Dividing Polynomials
Special Products continuedCube of a binomial
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(x + 2)3 = x3 + 6x2 + 12x + 8
(a – b)3 = a3 – 3a2b + 3ab2 – b3
(x – 2)3 = x3 – 6x2 + 12x – 8
![Page 8: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/8.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 3Find the product of (5y – 3)(5y + 3)
![Page 9: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/9.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 4Find the product of (4a + 7)2
![Page 10: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/10.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 5 Find the product of (m – 6)3
![Page 11: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/11.jpg)
6.4 – Multiplying and Dividing Polynomials
HOMEWORK
6.4 Worksheet
#1 - 18
![Page 12: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/12.jpg)
6.4 – Multiplying and Dividing Polynomials
Dividing PolynomialsYou can divide polynomials using
polynomial long divisionYou follow the same steps to divide
polynomials as you do to divide whole numbers
divide, multiply, subtract and bring downBefore dividing polynomials, make sure the
dividend and divisor are in standard form
![Page 13: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/13.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 6Find the quotient of 875 ÷ 31
![Page 14: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/14.jpg)
6.4 – Multiplying and Dividing Polynomials
Example 7Find the quotient of (3x3 + 17x2 + 21x – 11)
÷ (x + 3)
![Page 15: Chapter 6 – Polynomials and Polynomial Functions 6.4 – Multiplying and Dividing Polynomials.](https://reader036.fdocuments.in/reader036/viewer/2022071718/56649ef45503460f94c06a26/html5/thumbnails/15.jpg)
6.4 – Multiplying and Dividing Polynomials
HOMEWORK
6.4 Worksheet
#21 – 29