Polynomial Long Division

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.

You are now a third grader………..

….learning how to do long division for the first time.

4 2540

Does 4 divide into 2?No! So focus

on the 25.4 goes into 25 evenly 6

times.

6

Now, 6 times 4 is 24 so we put a 24 under the

25.

24

And NOW we subtract!

-241

And bring down the 4

and 0.

40

Repeat the process.

3

12-1220

5

16x- 51

You are now in Advanced Algebra

….learning how to do long division for the first time.

x2 – 3x + 5 3x 3 + 4x - 6

Step 1: Focus only on the first terms of both polynomials.Step 2: Decide WHAT you would multiply x2 to get a 3x3

3x(x2 -3x + 5) will give us 3x3 – 9x2 + 15x

3x

Step 3: NOW you will multiply x2 -3x + 5 by this 3x.

3x3 – 9x2 + 15x

WATCH OUT that you DON’T combine UNLIKE TERMS!

-3x3 + 9x2 - 15x

9x2 - 11x - 6 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

+ 9

9x2 -27x + 45- 9x2 +27x -45This is our

remainder and we write it in

fraction form as follows...

16x - 51 x2 - 3x + 5 +

Step 4: NOW since we are subtracting we change the signs of the BLUE polynomial!