To review Polynomial Long Division, watch the following set of YouTube videos introducing a review of long division, division by a monomial, long division of a polynomial by another polynomial, and synthetic division. The videos are followed by several practice problems for you to try, covering all the basic concepts covered in the videos, with answers and detailed solutions. Some additional resources are included for more practice at the end. 1. https://www.youtube.com/watch?v=txEyF2QzCqs (review of long division) 2. https://www.youtube.com/watch?v=nv_djIs0v2U (dividing by a monomial) 3. https://www.youtube.com/watch?v=Ih1wb6AxhMI (dividing by a binomial) 4. https://www.youtube.com/watch?v=FTRDPB1wR5Y (dividing polynomials) Note that this presenter is locating terms in the quotient slightly differently than the presenter in Video 3. Both methods are correct. 5. https://www.youtube.com/watch?v=lLgRS0mUZLw (synthetic division)
Practice problems: The following problems use the techniques demonstrated in the above videos. The answers are given after the problems. Then detailed solutions, if you need them, are provided after the answer section. For further assistance and help please contact Math Assistance Area.
3푥5 4푥7 1. a. Simplify: = ______b. Simplify: = ______2푥3 8푥2
6푥4+9푥3−3푥2+4푥+1 2. Divide: 3푥2
3. Divide: (푥4 + 3푥3 − 2푥2 − 3푥 + 1) ÷ (푥 + 2)
푥3−3푥2−4푥+12 4. = ______푥−3
8푥3+2푥2+1 5. Divide: 2푥2−푥
푥6−64 6. Use long division: 푥−2
______
Stop by or call (630) 942-3339
3 2푥4+푥3+푥− 4 7. Divide: 1 푥− 2
4푥5+13푥4+108푥2−81 8. Divide: 푥2+9
9. Find (5푥4 + 5푥2 + 5) ÷ (푥2 − 푥 + 1)
10. The difference of cubes factoring pattern can be easily forgotten, but can be derived by doing the
푎3−푏3 following long division problem: = ______. So 푎3 − 푏3 = (푎 − 푏)(______) 푎−푏
11. Redo the division in Question #3 using synthetic division.
12. Redo Question #6 using synthetic division.
Answers:
3 푥5 4푥+1 9 1. a. 푥2 b. 2. 2푥2 + 3푥 − 1 + 3. 푥3 + 푥2 − 4푥 + 5 − 2 2 3푥2 푥+2
4. 푥2 − 4 (remainder = 0)
푥3−3푥2−4푥+12 Note: Since = 푥2 − 4, then 푥3 − 3푥2 − 4푥 + 12 = (푥 − 3)(푥2 − 4). 푥−3
(푥 − 3) is a factor of 푥3 − 3푥2 − 4푥 + 12.
3푥+1 5. 4푥 + 3 + 6. 푥5 + 2푥4 + 4푥3 + 8푥2 + 16푥 + 32 2푥2−푥
3 324푥 7. 2푥3 + 2푥2 + 푥 + 8. 4푥3 + 13푥2 − 36푥 + 9 − 2 푥2+9
9. 5푥2 + 5푥 + 5 10. (푎2 + 푎푏 + 푏2)
11. (same as Q. 3) 12. (same as Q. 6)
______
Stop by or call (630) 942-3339
Detailed Solutions
______
Stop by or call (630) 942-3339
______
Stop by or call (630) 942-3339
______
Stop by or call (630) 942-3339
______
Stop by or call (630) 942-3339
______
Stop by or call (630) 942-3339
Additional Resources Click on the links below to download a free online worksheet for more practice: 1. Go To https://cdn.kutasoftware.com/Worksheets/Alg1/Dividing%20Polynomials.p df
2. For more help please contact the Math Assistance Area.
______
Stop by or call (630) 942-3339