1 / 18

Dividing Polynomials

Dividing Polynomials. Simple Division -. dividing a polynomial by a monomial. Simplify. Simplify. Long Division -. divide a polynomial by a polynomial. Think back to long division from 3rd grade. How many times does the divisor go into the dividend? Put that number on top.

alia
Download Presentation

Dividing Polynomials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dividing Polynomials

  2. Simple Division - dividing a polynomial by a monomial

  3. Simplify

  4. Simplify

  5. Long Division - divide a polynomial by a polynomial • Think back to long division from 3rd grade. • How many times does the divisor go into the dividend? Put that number on top. • Multiply that number by the divisor and put the result under the dividend. • Subtract and bring down the next number in the dividend. Repeat until you have used all the numbers in the dividend.

  6. x - 8 + 3x -( ) x2 - 8x - 24 -( ) - 8x - 24 0

  7. h2 + 4h + 5 -( ) - 4h2 h3 - 11h 4h2 -( ) 4h2 - 16h 5h + 28 -( ) 5h - 20 48

  8. Synthetic Division - divide a polynomial by a polynomial • To use synthetic division: • There must be a coefficient for every possible power of the variable. • The divisor must have a leading coefficient of 1.

  9. Since the numerator does not contain all the powers of x, you must include a 0 for the Step #1: Write the terms of the polynomial so the degrees are in descending order.

  10. 5 0 -4 1 6 Step #2: Write the constant r of the divisor x-r to the left and write down the coefficients. Since the divisor is x-3, r=3

  11. 5 Step #3: Bring down the first coefficient, 5.

  12. Step #4: Multiply the first coefficient by r, so and place under the second coefficient then add. 15 5 15

  13. 15 45 15 5 Step #5: Repeat process multiplying the sum, 15, by r; and place this number under the next coefficient, then add. 41

  14. 15 45 123 372 15 41 5 Step #5 cont.: Repeat the same procedure. Where did 123 and 372 come from? 124 378

  15. 15 45 123 372 15 41 124 378 5 Step #6: 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.

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

  17. Ex 7: Step#1: Powers are all accounted for and in descending order. Step#2: Identify r in the divisor. Since the divisor is x+4, r=-4 .

  18. Step#3: Bring down the 1st coefficient. Step#4: Multiply and add. Step#5: Repeat. 4 -4 20 0 8 -1 1 0 -2 10 -5

More Related