# How do you divide #(x^4+x^2-3x-3)/(5x-2)#?

##### 1 Answer

Long divide the coefficients of the polynomials to find:

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

#= 1/5x^3+2/25x^2+29/125x-317/625 - 2509/(625(5x-2))#

#### Explanation:

I like to divide polynomials by long dividing their coefficients, including

This is similar to long division of numbers.

Write the dividend

Write each term of the quotient in turn, chosen to match the leading term of the running remainder when multiplied by the divisor.

So we write

Subtract the product from the dividend and bring down the next term of the dividend alongside the result as the running remainder.

Choose the next term

Repeat until the running remainder is shorter than the divisor and there is no remaining term to bring down from the dividend. This is the final remainder.

In this particular example we find that the quotient polynomial is:

#1/5x^3+2/25x^2+29/125x-317/625#

with remainder

That is:

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

#= 1/5x^3+2/25x^2+29/125x-317/625 - 2509/(625(5x-2))#

or if you prefer:

#x^4+x^2-3x-3#

#= (5x-2)(1/5x^3+2/25x^2+29/125x-317/625)-2509/625#