# How do you divide #( 6x^3 + 10x^2 + x + 8)/(2x^2 + 1)#?

##### 1 Answer

Long divide the coefficients to find quotient

#### Explanation:

I like to long divide the coefficients like this:

...not forgetting to include a

In this example we find the quotient is

The process is similar to long division of numbers:

Write the dividend (

Write the divisor (

Start writing the quotient, term by term, choosing each successive term to match the leading term of the running remainder:

The first term of the quotient is

We then write out the product

We choose the next term of the quotient

We then write out the produce

There are no more terms to bring down from the dividend, so this is our final remainder.

Then interpret the coefficient sequences by applying them to the appropriate powers of

#(6x^3+10x^2+x+8)/(2x^2+1) = 3x+5+(-2x+3)/(2x^2+1)#

Or if you prefer:

#6x^3+10x^2+x+8 = (3x+5)(2x^2+1)+(-2x+3)#