1. Polynomial Long Division

2. We can use polynomial long division to help us find the factors of a polynomial.
And we know that FACTORS help us find x intercepts and solutions!
This is what we were using long division in grade school for….
I know you though it was to find how many times 4 goes into say, 36. And I know you know the answer is 9. But remember 9 and 4 are factors of 36.

3. 6 3 5 4 2540 -24 24 1 40 -12 12 20 You are now a third grader………..
Now, 6 times 4 is 24 so we put a 24 under the 25.
….learning how to do long division for the first time.
Repeat the process.
Does 4 divide into 2?
No! So focus on the 25.
And bring down the 4 and 0.
4 goes into 25 evenly 6 times.
And NOW we subtract! 6 3 5 4
2540
-24 24 1 40
-12 12 20

4. 3x + 9 16x - 51 + 3x 3 + 4x - 6 -3x3 + 9x2 - 15x 3x3 – 9x2 + 15x
You are now in Advanced Algebra
….learning how to do long division for the first time.
16x - 51
x2 - 3x + 5 3x
+ 9 +
x2 – 3x + 5
3x 3 + 4x - 6
-3x3 + 9x2 - 15x
3x3 – 9x2 + 15x
9x x - 6
This is our remainder and we write it in fraction form as follows...
Step 2: Decide WHAT you would multiply x2 to get a 3x3
WATCH OUT that you DON’T combine UNLIKE TERMS!
Step 4: NOW since we are subtracting we change the signs of the BLUE polynomial!
- 9x2 +27x -45
Step 5: NOW we repeat the process. 9 times x2 will give us 9x2 and 9 times x2 -3x + 5 will give us 9x2 – 27x + 45
9x2 -27x + 45
Step 3: NOW you will multiply x2 -3x + 5 by this 3x.
Step 1: Focus only on the first terms of both polynomials.
3x(x2 -3x + 5) will give us 3x3 – 9x2 + 15x
16x- 51