What is the point of synthetic division?

In summary, the conversation discusses the use of synthetic division for polynomial division and whether it is worth teaching or not. Some individuals argue that it is a faster and more efficient method while others believe it is unnecessary and can lead to confusion for students. The conversation also touches on the practicality of knowing the algorithm versus understanding why it works.
  • #1
harvellt
95
0
So I was tutoring a friend who is in college algebra and we were working threw synthetic division of polynomials, and I realized I have never used that technique after pre-calc. I think its easier and there is less chance of sign mistakes using good old long division for polynomials why are we wasting valuable classroom time teaching this technique when it is just a "short cut" (not really) for something that is equally easy and works better?
 
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  • #2
If you think both ways are equally easy, then by all means do whatever you like. I feel that synthetic division saves enough time that it's worth the entire 10 minutes it takes to explain the process. Saves paper too.
 
  • #3
Synthetic Division can and often is FASTER than regular-form polynomial division. Less symbols need to be written, but one must know how to perform the algorithm. Also, the resulting remainder which may occur is more immediately meaningful (related to the Remainder and Factor Theorems).
 
  • #4
Lik the OP, I haven't really used synthetic division since I learned it, and I feel that the 'checks' built into the long method help me to avoid mistakes. But synthetic division is faster -- and if I needed to do more polynomial divisions I'd probably start doing it synthetically.
 
  • #5
As a calculus teacher, this problem strikes home with me. Synthetic division is faster when it's applicable, but students often try to apply it to situations where the divisor is not linear, and become hopelessly lost. I think they should stick to long division.
 
  • #6
Knowing the algorithm isn't all that practical but understanding why it works is.
 
  • #7
Even though I don't particularly care for synthetic division, I absolutely agree with you.
 
  • #8
rochfor1 said:
As a calculus teacher, this problem strikes home with me. Synthetic division is faster when it's applicable, but students often try to apply it to situations where the divisor is not linear, and become hopelessly lost. I think they should stick to long division.

It is not too hard to devise a synthetic division algorithm that works with quadratic and higher-degree divisors. I worked it out back in high school.

However, like everyone else, I haven't had any need for synthetic division since then.
 
  • #9
hella useful in residue theory n junk`
 

1. What is synthetic division?

Synthetic division is a method used in algebra to divide polynomials without using long division. It is a quicker and more efficient way of dividing polynomials, especially when dividing by a linear factor.

2. How is synthetic division different from long division?

Synthetic division is different from long division in that it only requires the coefficients of the polynomial, while long division also requires the variables. Additionally, synthetic division is a shorter and simpler process compared to long division.

3. When is synthetic division used?

Synthetic division is often used when dividing polynomials by a linear factor, as it is a faster and easier method compared to long division. It is also useful for finding roots and factors of a polynomial.

4. What is the point of using synthetic division?

The main point of using synthetic division is to simplify the process of dividing polynomials. It allows for quicker calculation of roots and factors, and can also be used to evaluate polynomials at a given value.

5. Can synthetic division be used for all polynomials?

No, synthetic division can only be used for dividing polynomials by a linear factor. If the polynomial is not divisible by a linear factor, long division or other methods may need to be used.

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