1. Long Division

2. What is a Polynomial?
Remember, a polynomial is just a number of terms separated by + and – signs.
A term isn’t allowed to be anything too funky, so a polynomial doesn’t have any really weird parts. This is an ordinary polynomial:

3. What is a Binomial?
“Binomial” is just another name for a polynomial with 2 terms.

4. A Division Problem
What if they ask us to divide a polynomial by a binomial?
We would have to use long division:

5. Long Division
Remember long division from grade school?

6. It’s not that hard!
Just break it into parts.
Take the outside number into the beginning of the inside number.

7. Same here
Take the outside number into the beginning of the inside number.

8. It’s not that hard!
What number times 12 gives a number close to (but not bigger than) 62?

9. Same here
What times x would give you

10. Now multiply
Multiply the top times the outside number:

11. Same here
Multiply the top times the whole outside:
Common mistake: Forgetting to multiply the 2

12. Now subtract
Change the sign on the bottom and combine

13. Same here
Change the signs on the bottom and combine:

14. Bring it on!
Bring down the next number

15. Same here
Bring down the rest of the number

16. Rinse and repeat
Here we go again – first into first

17. Same here
Here we go again – first into first

18. Rinse and repeat
Here we go again – multiply

19. Same here
Here we go again – first into first

20. Rinse and repeat
Here we go again – change the signs on the bottom and combine

21. Same here
Here we go again – change the signs on the bottom and combine

22. Things that can be weird
Remainders:
If you don’t get zero as a remainder, make a fraction with the remainder as the top and the outside polynomial as the bottom.

23. Things that can be weird
Remainders:
If you don’t get zero as a remainder, make a fraction with the remainder as the top and the outside polynomial as the bottom.

24. Things that can be weird
Missing pieces:
If your polynomial is missing pieces, fill in with zeros as place-holders.

25. Things that can be weird
Out of order:
Make sure your polynomial is written with the exponents in order from biggest to smallest.

26. Long Division Be sure polynomials are in descending order of exponents
Take the first part into the first part.
Multiply
Change the signs on the bottom and combine.
Bring down the rest of the “inside”.
Rinse and repeat.