1. Polynomial Long Division

2. 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. You are now a third grader……….. ….learning how to do long division for the first time. 42540 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! -24 1 And bring down the 4 and 0. 40 Repeat the process. 3 12-12 20 5

4. 16x- 51 You are now in Advanced Algebra ….learning how to do long division for the first time. x 2 – 3x + 5 3x 3 + 4x - 6 Step 1: Focus only on the first terms of both polynomials. Step 2: Decide WHAT you would multiply x 2 to get a 3x 3 3x(x 2 -3x + 5) will give us 3x 3 – 9x 2 + 15x 3x Step 3: NOW you will multiply x 2 -3x + 5 by this 3x. 3x 3 – 9x 2 + 15x WATCH OUT that you DON’T combine UNLIKE TERMS! -3x 3 + 9x 2 - 15x 9x 2 - 11x - 6 Step 5: NOW we repeat the process. 9 times x 2 will give us 9x 2 and 9 times x 2 -3x + 5 will give us 9x 2 – 27x + 45 + 9 9x 2 -27x + 45 - 9x 2 +27x -45 This is our remainder and we write it in fraction form as follows... 16x - 51 x 2 - 3x + 5 + Step 4: NOW since we are subtracting we change the signs of the BLUE polynomial!