# What is the point of synthetic division?

#### harvellt

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?

#### Tobias Funke

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.

#### symbolipoint

Homework Helper
Gold Member
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).

#### CRGreathouse

Homework Helper
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.

#### rochfor1

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.

#### qntty

Knowing the algorithm isn't all that practical but understanding why it works is.

#### rochfor1

Even though I don't particularly care for synthetic division, I absolutely agree with you.

#### Ben Niehoff

Gold Member
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.

#### dipstik

hella useful in residue theory n junk`

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving