조립제법

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  1. Synthetic division carries this simplification even a few more steps.[1]
  2. In synthetic division, only the coefficients are used in the division process.[1]
  3. How To: Given two polynomials, use synthetic division to divide Write k for the divisor.[1]
  4. Show Solution Begin by setting up the synthetic division.[1]
  5. Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor — and it only works in this case.[2]
  6. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.[2]
  7. In the synthetic division, I divided by x = −3, and arrived at the same result of x + 2 with a remainder of zero.[2]
  8. The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper than long division.[3]
  9. The above form of synthetic division is useful in the context of the polynomial remainder theorem for evaluating univariate polynomials.[3]
  10. Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm.[4]
  11. For an example of synthetic division, consider dividing by .[4]
  12. (x - 3) , let's compare long division to synthetic division to see where the values are the same.[5]
  13. As was done with long division, synthetic division must also fill in missing terms in the dividend.[5]
  14. Let's see what happens if we use our regular synthetic division process, and ignore the fact that the leading coefficient of the divisor is 2 (not 1).[5]
  15. Now, we have an equivalent problem where the denominator resembles what we have seen previously in our synthetic division questions (a leading coefficient of one).[5]
  16. We use synthetic division to evaluate polynomials by the remainder theorem, wherein we evaluate the value of \(p(x)\) at \(a\) while dividing \((\frac{p(x)}{(x – a)})\).[6]
  17. Among these two methods, the shortcut method to divide polynomials is the synthetic division method.[7]
  18. In the synthetic division method, we will perform multiplication and addition, in the place of division and subtraction, which is used in the long division method.[7]
  19. The process of the synthetic division will get messed up if the divisor of the leading coefficient is other than one.[7]
  20. Frequently Asked Questions on Synthetic Division What is meant by synthetic division?[7]
  21. Synthetic division is a simplified method of dividing a polynomial by another polynomial of the first degree.[8]
  22. However, synthetic division uses only the coefficients and requires much less writing.[9]
  23. To understand synthetic division, we walk you through the process below.[9]
  24. In this case, we use 0 as placeholders when performing synthetic division.[9]
  25. In this case, a shortcut method called synthetic division can be used to simplify the rational expression.[10]
  26. It is a Super Fun way to engage students in practice and review of synthetic division and the remainder theorem.[11]
  27. Solution: This one is a little tricky, because we can only do synthetic division with a linear binomial with no leading coefficient, and this divisor has a leading coefficient of 2.[12]
  28. So we can't use synthetic division.[12]
  29. However, we can use synthetic division using the binomial (x - 1/2).[12]
  30. It turns out that we often use synthetic division when trying to find roots, and if (2x - 1) is a factor, then so is (x - 1/2), so it works out well to do this.[12]
  31. Luckily there is something out there called synthetic division that works wonderfully for these kinds of problems.[13]
  32. In order to use synthetic division we must be dividing a polynomial by a linear term in the form \(x - r\).[13]
  33. Example 2 Use synthetic division to divide \(5{x^3} - {x^2} + 6\) by \(x - 4\).[13]
  34. Show Solution Okay with synthetic division we pretty much ignore all the \(x\)’s and just work with the numbers in the polynomials.[13]
  35. Synthetic division is a shortcut way of dividing polynomials.[14]
  36. Synthetic division is most commonly used when dividing by linear monic polynomials x - b .[14]
  37. Keep in mind that synthetic division works for any polynomial divisors: for non-monic polynomials as well as for polynomials of degrees higher than one.[14]
  38. So, let's dive in and learn how to divide polynomials using synthetic division![14]
  39. Here is how to do this problem by synthetic division.[15]
  40. We will use synthetic division to divide f(x) by x + 4.[15]
  41. Use synthetic division to divide f(x) by x − 7.[15]
  42. Use synthetic division to divide g(x) by x + 2.[15]
  43. Synthetic division can make life easier when you are dividing polynomials.[16]
  44. So, can you use synthetic division with a coefficient that is not 1?[16]
  45. You need a monic linear divisor to use synthetic division.[16]
  46. You can also divide by a quadratic divisor by using synthetic division repeatedly.[16]
  47. One way is to use synthetic division.[17]
  48. You could’ve used synthetic division to do this, because you still get a remainder of 100.[17]
  49. Throw them out with synthetic division![18]
  50. Then we are ready to use synthetic division.[19]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Synthetic Division
  2. ↑ 2.0 2.1 2.2 How does synthetic division of polynomials work?
  3. ↑ 3.0 3.1 Synthetic division
  4. ↑ 4.0 4.1 Synthetic Division -- from Wolfram MathWorld
  5. ↑ 5.0 5.1 5.2 5.3 Polynomial Synthetic Division
  6. ↑ How to Divide Polynomials Using Synthetic Division?
  7. ↑ 7.0 7.1 7.2 7.3 Synthetic Division (Definition, Steps and Examples)
  8. ↑ Steps & Examples - Video & Lesson Transcript
  9. ↑ 9.0 9.1 9.2 OpenAlgebra.com: Synthetic Division
  10. ↑ The Difference Between Long Division & Synthetic Division of Polynomials
  11. ↑ Synthetic Division Teaching Resources
  12. ↑ 12.0 12.1 12.2 12.3 Synthetic Division: Polynomials
  13. ↑ 13.0 13.1 13.2 13.3 Dividing Polynomials
  14. ↑ 14.0 14.1 14.2 14.3 Synthetic Division Calculator With Steps
  15. ↑ 15.0 15.1 15.2 15.3 Topics in precalculus
  16. ↑ 16.0 16.1 16.2 16.3 Synthetic Division With Coefficient Not 1 (Or A Quadratic Divisor) – JDM Educational
  17. ↑ 17.0 17.1 How to Guess and Check Real Roots — 3 — Testing Roots by Dividing Polynomials Using Synthetic Division
  18. ↑ What is Synthetic Division?
  19. ↑ Synthetic division

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  • [{'LOWER': 'synthetic'}, {'LEMMA': 'division'}]
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