1. ## Synthetic Division

Why can't synthetic division work if the variable of the divisor is quadratic or greater?

SAMPLE:

We can apply synthetic divsion to the rational expression

(3x^2 - 4x + 5)/(x + 4)

But why can't we apply synthetic division in the following sample:

(3x^2 - 4x + 5)/(x^2 + 4)?

Thanks

2. hmm...

Ok, let say 4 divided by 2 you will get 2.
1 divided by 2 you will get a decimal number because the divisor is greater than the dividend..

so when you're dealing with polynomials is it possible for you to get an answer in decimal if the divisor is greater than the dividend?
the degree of the divisor must be less than or equal the degree of the dividend..

correct me if i was wrong..

3. Originally Posted by magentarita
Why can't synthetic division work if the variable of the divisor is quadratic or greater?

SAMPLE:

We can apply synthetic divsion to the rational expression

(3x^2 - 4x + 5)/(x + 4)

But why can't we apply synthetic division in the following sample:
$\displaystyle \frac{(3x^2 - 4x + 5)}{(x^2 + 4)}$?

Thanks
Synthetic division is used to test potential roots/zeroes of a polynomial OR if you already know at least one of the roots of your polynomial, you can use the known root as the divisor and use synthetic division to find other roots.

You usually use synthetic division to prove that a number is a root of your polynomial. x=-4 is a potential root/zero of the polynomial $\displaystyle (3x^2 - 4x +5)$. If you get a remainder of 0 when you divide the polynomial by -4, then x= -4 IS a root of your polynomial.

You could not use synthetic div. on the second problem, because the polynomials are of the same degree. They are both quadratics. Synthetic div. is basically a short hand version of long division and it is also used to reduce large degree polynomials.

Long story short: synthetic division is only used when you are dividing a polynomial of degree 2 or more by a linear equation (ex. (x+2)) Otherwise you must use traditional long division.

FYI, the polynomial you have above does not have any roots!! It never crosses the x axis!

4. ## Thanks

I want to thank both replies for your help and input.