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.

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

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 9x2 - 11x - 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