Synthetic Division: Proving It Works

Thread starter soandos
Start date Oct 9, 2008
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Division

In summary, synthetic division is a method used for dividing a polynomial by a linear expression. It simplifies the process and is more efficient than long division. It can only be used for dividing by a linear expression with a degree of 1 and the remainder should be zero if done correctly. Some limitations include only being able to divide polynomials with real coefficients and not being able to perform other operations.

Oct 9, 2008

soandos

is there a way to prove it?
if so what is it.

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Oct 9, 2008

CRGreathouse

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It is identical to normal division and proved the same way.

Oct 10, 2008

soandos

how so? in synthetic, it is add and multiply, and in regular, it is divide and subtract.

1. How does synthetic division work?

Synthetic division is a method used to divide a polynomial by a linear expression, also known as a binomial. It involves a series of steps that use coefficients from the polynomial to determine the quotient and remainder.

2. What is the purpose of synthetic division?

The main purpose of synthetic division is to simplify the process of polynomial division. It is a quicker and more efficient method compared to long division, especially for polynomials with higher degrees.

3. Can synthetic division be used for any type of polynomial?

No, synthetic division can only be used when dividing by a linear expression, meaning a binomial with a degree of 1. It cannot be used for polynomials with a degree higher than 1 or for dividing by a polynomial with multiple terms.

4. How do you know if you have correctly performed synthetic division?

If you have correctly performed synthetic division, the remainder should be equal to zero. This means that the linear expression used as the divisor is a factor of the polynomial, and the resulting quotient is the other factor.

5. Are there any limitations to using synthetic division?

One limitation of synthetic division is that it can only be used for dividing polynomials with real coefficients. It cannot be used if the polynomial has complex or imaginary roots. Additionally, it can only be used for division, not for multiplication or other operations.