1. Section 3 Dividing Polynomials
Chapter 6
Section 3
Dividing Polynomials

2. Long Division Vocabulary Reminders

3. Remember Long Division
Does 8 go into 6? No
Does 8 go into 64?
Yes, write the integer on top.
Multiply 8∙8
Write under the dividend
Subtract and Carry Down
How many times does 8 go into 7 evenly?
0 write over the 7
Multiply 0∙8
Subtract and write remainder as a fraction.

4. The divisor and quotient are only FACTORS if the remainder is Zero.

5. Examples with variables

6. Examples
If the divisor has more than one term, always use the term with the highest degree.
A remainder occurs when the degree of the dividend is less than the degree of the divisor

7. Example:

8. Try These Examples Divide using long division.

9. Long division of polynomials is tedious!
Lets learn a simplified process! This process is called Synthetic Division
p. 316 It may look complicated, but watch a few examples and you will get the hang of it.

10. Use synthetic division to divide 3x3-4x2+2x-1 by x+1
Reverse the sign of the constant term in the divisor. Write the coefficients of the polynomial in standard form (Remember to include zeros)
Translation: Instead of write
Bring down the first coefficient
Multiply the first coefficient by the new divisor. Add.
Repeat step 3 until the end. The last number is the remainder.
NOW write the polynomial.
To write the answer use one less degree than the original polynomial.

11. Example: Use synthetic division to divide
x3+4x2+x-6 by x+1
x3-2x2-5x+6 by x+2

12. Remainder Theorem
If a polynomial is being divided by (x-a) then the remainder is P(a).
Example: Use the remainder theorem to find P(-4) for P(x)=x3-5x2+4x+12
DO NOT change the number P(a) to -a

13. Try This Problem
Use synthetic division to find P(-1) for P(x)=4x4+6x3-5x2-60

14. Homework
Practice 6.3 Evens