1. Section 5.5

2. Dividing a Polynomial by a Polynomial The objective is to be able to divide a polynomial by a polynomial by using long division. Dividend – the number which is being divided. Divisor – The number that is being divided into the dividend. Quotient – The result obtained when numbers or expressions are divided. Remainder – The part that is left over when the divisor no longer goes into the dividend a whole number of times.

3. Polynomial Long Division Step 1: Write it as you would a regular long division problem. The x+2 is the divisor and the x 2 +3x-1 is the dividend.

4. Step 2 x xx x   2 1 1xxx  23 2 2 - Divide x 2 by x to get x. Place this on top. Multiply x+2 by x to get x 2 +2x. Subtract the x 2 +2x from the x 2 +3x-1.

5. Step 3 Divide the x by x to get 1. Multiply x+2 by 1 to get x+2. Subtract x+2 from the x-1. x   2 3 -  1 -   3 2 2 2 xxx x xx x   21 1

6. Step 4 Write your final answer. The x+1 is the quotient.

7. AA

8. xxx x xx x x       215 3 2 3 36 9 2 2 - - X 2 divided by x is x. Multiply x-2 by x. Subtract 3x divided by x is 3. Multiply x-2 by 3. Subtract You Try It

9. 32x 1041125 2 xxx   3 2 xx  -  810x - 82 x   8 12x 2 divided by 4x is 3x. Multiply 4x-1 by 3x. Subtract 8x divided by 4x is 2. Multiply 4x-1 by 2. Subtract You Try It

11. Let’s look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient of 1. #1#2

12. Step #1: Write the terms of the polynomial so the degrees are in descending order.

13. Step #2: Write the constant a of the divisor x- a to the left and write down the coefficients.

14. Step #3: Bring down the first coefficient, 5. Step #4: Multiply the first coefficient by r (3*5).

15. Step #5: After multiplying in the diagonals, add the column. Add the column

16. Multiply the diagonals, add the columns. Add

17. Step #7: Repeat the same procedure as step #6. Add Colum ns

18. Step #8: 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.

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

20. Try this one: