Synthetic Division: Divide Polynomials by Monomials

  • Thread starter soandos
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Synthetic division is not limited to "monomials". You can use it to divide by any linear polynomial. There is also a "general" polynomial division algorithm. And that can be used to divide by any polynomial. It is just much more complicated. So, in summary, synthetic division can be used to divide polynomials by monomials, as well as any linear polynomial. However, for dividing by more complex polynomials, a general polynomial division algorithm must be used.
  • #1
soandos
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so synthetic division can be used to divide polynomials by monomials. is there a to divide by
ax-b as opposed to x-b? ax^2-b? is there a general rule?
thanks.
or does one have to revert to polynomial long division.
 
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  • #2
"Synthetic division" is used specifically to divide a polynomial by "x- a" for some number a. That is a very important special case since it is so often important to find all roots of a polynomial equation and dividing by x-a when a is a root you have already found reduces the equation.

Of course, you can use regular algebraic division if the divisor is something like 3x- 2 or [itex]x^2+ 4x- 3[/itex].
 

1. What is synthetic division?

Synthetic division is a method used to divide polynomials by monomials. It is a simplified form of long division that is useful for quickly solving polynomial equations.

2. How does synthetic division work?

Synthetic division involves setting up a table with the coefficients of the polynomial being divided and the divisor. The first step is to bring down the first coefficient of the polynomial and then multiply it by the divisor. The product is then written below the next coefficient and added to it. This process is repeated until all the coefficients have been accounted for. The final result is the quotient of the division.

3. When is synthetic division used?

Synthetic division is used when dividing a polynomial by a monomial, which means the divisor is a single term with a variable raised to a power. This method is especially helpful when the divisor is a binomial with a leading coefficient of 1.

4. What are the advantages of using synthetic division?

Synthetic division is a quicker and more efficient method of dividing polynomials compared to traditional long division. It also eliminates the need for dealing with exponents and simplifying the quotient, making it easier to solve polynomial equations.

5. Are there any limitations to synthetic division?

Synthetic division can only be used to divide polynomials by monomials, so it is not suitable for dividing by polynomials with more than one term. It also cannot be used to find the remainder of a division, as it only gives the quotient.

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