- #1
streetmeat
- 8
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How do i know under which circumstances to use synthetic and when to just do regular polynomial division? do they not both give the same results?
derekjn said:Synthetic division only works if you are dividing a polynomial by a linear factor..
Synthetic division is a method used to divide polynomials by a binomial of the form (x - a). It is a quicker and more efficient method compared to long division, which involves dividing each term of the polynomial by the divisor and then subtracting the remainder.
Synthetic division is only applicable when dividing by a binomial of the form (x - a). If the divisor is not in this form, then long division should be used. Additionally, synthetic division can only be used when the degree of the polynomial being divided is one more than the degree of the divisor.
The steps for synthetic division are as follows:
1. Set up the division problem by writing the coefficients of the polynomial in descending order.
2. Write the constant term of the divisor on the left side of the division bar.
3. Bring down the first coefficient of the dividend (the polynomial being divided) and write it on the right side of the division bar.
4. Multiply the constant term of the divisor by the coefficient just brought down and write the result below the next coefficient of the dividend.
5. Add this new term to the next coefficient of the dividend and write the result below.
6. Repeat this process until all coefficients of the dividend have been used. The final result will be the quotient.
Yes, synthetic division always gives the same result as long division. However, it is important to note that synthetic division can only be used for specific types of polynomial division, as mentioned in the answer to question 2.
No, synthetic division can only be used for division problems with no remainders. If there is a remainder, long division must be used to accurately solve the problem.