Ex 4: Divide a Polynomial by a Binomial Using Synthetic Division — Transcript

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1. 0:00- WE'RE GOING TO PERFORM THIS DIVISION
2. 0:02USING SYNTHETIC DIVISION
3. 0:03AND BECAUSE WE'RE DIVIDING OUR POLYNOMIAL BY A BINOMIAL
4. 0:07IN THE FORM OF X - K,
5. 0:10SYNTHETIC DIVISION IS AN ALTERNATIVE
6. 0:12TO PERFORMING LONG DIVISION.
7. 0:14SO THE FIRST STEP IS TO LIST THE COEFFICIENTS OF OUR DIVIDEND.
8. 0:18SO IF OUR POLYNOMIAL IS GIVEN IN THIS FORM,
9. 0:21WE'RE GOING TO LIST THEM HORIZONTALLY
10. 0:23AS "A", B, C, AND D.
11. 0:26NOTICE HOW THE TERMS ARE IN DESCENDING ORDER
12. 0:29AND IF ANY OF THESE TERMS ARE MISSING
13. 0:30WE WILL HAVE TO INCLUDE A ZERO COEFFICIENT.
14. 0:33LOOKING AT OUR DIVISION PROBLEM
15. 0:34SINCE WE HAVE X CUBE + 8 DIVIDED BY THE QUANTITY X + 2,
16. 0:39WE NEED TO THINK OF THIS AS X CUBED PLUS--
17. 0:43NOTICE HOW THERE'S NO X SQUARED TERM, SO WE HAVE 0 X SQUARED.
18. 0:48THERE'S ALSO NO X TERM,
19. 0:50SO WE'LL HAVE 0 X + 8 DIVIDED BY THE QUANTITY X + 2.
20. 0:58SO WHEN LISTING THE COEFFICIENTS WE'LL HAVE 1, ZERO, ZERO AND 8.
21. 1:12THE NEXT STEP IF WE'RE DIVIDING BY X - K,
22. 1:15WE WANT K OUT HERE ON THE LEFT
23. 1:17AND NOTICE THESE ARE OPPOSITE SIGNS.
24. 1:19SO IF WE'RE DIVIDING BY X + 2, K IS ACTUALLY GOING TO BE -2.
25. 1:25AGAIN, THE CONSTANT OF OUR DIVISOR
26. 1:28IS ALWAYS THE OPPOSITE SIGN OF THE VALUE
27. 1:30WE'RE GOING TO USE HERE.
28. 1:32AND NOW TO START SYNTHETIC DIVISION,
29. 1:33WE'RE GOING TO START BY BRINGING THIS TERM DOWN.
30. 1:36THEN EVERY TIME WE HAVE A TERM DOWN HERE AT THE BOTTOM
31. 1:39WE'RE GOING TO MULTIPLY IT BY -2
32. 1:42AND THEN MOVE IT TO THE NEXT COLUMN.
33. 1:44SO 1 x -2 IS -2.
34. 1:48SO WE'LL HAVE A -2 HERE,
35. 1:50AND THEN WE ADD VERTICALLY AND REPEAT THE PROCESS.
36. 1:53SO 0 + -2 IS -2.
37. 1:56THEN -2 x -2 IS 4.
38. 2:01ADD VERTICALLY, SO 0 + 4 IS 4, AND THEN 4 x -2 = -8.
39. 2:10ADD AND WE HAVE ZERO.
40. 2:13THIS LAST TERM IS OUR REMAINDER,
41. 2:15SO WE CAN SEE THAT X + 2 DOES DIVIDE EVENLY INTO X CUBED + 8,
42. 2:20BUT WE CAN ALSO DETERMINE THE DEGREE OF OUR QUOTIENT
43. 2:23BY TAKING THE DEGREE OF OUR DIVIDEND
44. 2:25AND SUBTRACTING THE DEGREE OF OUR DIVISOR.
45. 2:30AND SINCE 3 - 1 = 2,
46. 2:32THIS REPRESENTS THE COEFFICIENT OF THE DEGREE 2 TERM.
47. 2:36THIS REPRESENTS THE COEFFICIENT OF THE DEGREE 1 TERM.
48. 2:40THIS WOULD BE THE COEFFICIENT
49. 2:41OF OUR DEGREE ZERO TERM OR CONSTANT
50. 2:43AND HERE IS OUR REMAINDER.
51. 2:45SO OUR QUOTIENT IS EQUAL TO 1X SQUARED - 2X + 4.
52. 2:55AND NORMALLY IF WE HAVE A COEFFICIENT OF 1
53. 2:57WE LEAVE IT OFF, SO THIS WOULD BE OUR QUOTIENT,
54. 3:01AND BECAUSE THE REMAINDER IS ZERO WE KNOW THAT X + 2
55. 3:04IS A FACTOR OF X CUBED + 8.
56. 3:09OKAY, I HOPE YOU FOUND THIS HELPFUL.