1. 1-22-15 Bellwork  Divide (No Calculators)  1. 8,790÷2  2. 549,876÷32  3. 9,802,105÷30 Multiply #4 4. (5x-6)(2x+3)

2. Bellwork Solutions 

3. Dividing Polynomials Lesson 4-3

4. Dividing Polynomials: Simple Division When dividing polynomials, rewrite the expression by breaking it up based on the number of terms in the numerator. After breaking up the expression, simplify each term.

5. Dividing by a Monomial If the divisor only has one term, split the polynomial up into a fraction for each term. divisor Now reduce each fraction. 3x33x3 4x24x2 x2 1111

6. Dividing Polynomials ProblemBreak upSimplify ProblemBreak upSimplify

7. Dividing Polynomials Sometime division can be expressed like. Rewrite the problem as a fraction and solve like normal. ProblemRewriteBreak upSimplify

8. Simple Division – More Practice dividing a polynomial by a monomial

9. Simplify

11. 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.

12. -( ) x x2x2 + 3x - 8x - 8 - 24 - 8x- 24 0 -() x 2 /x = x -8x/x = -8

13. Synthetic Division - 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. divide a polynomial by a polynomial

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

15. 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 50-416

16. 5 Step #3: Bring down the first coefficient, 5.

17. 5 Step #4: Multiply the first coefficient by r, so and place under the second coefficient then add. 15

18. 5 Step #5: Repeat process multiplying the sum, 15, by r; and place this number under the next coefficient, then add. 45 41

19. 5 15 45 41 Step #5 cont.: Repeat the same procedure. 123 124 372 378 Where did 123 and 372 come from?

20. 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. 5 15 45 41 123 124 372 378

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

22. 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.

23. Step#3: Bring down the 1st coefficient. Step#4: Multiply and add. -5 Step#5: Repeat. 20 4-4 0 8 10-210

24. Ex 8: Notice the leading coefficient of the divisor is 2 not 1. We must divide everything by 2 to change the coefficient to a 1.

25. 1-22-15 Homework #’s 1-4