# How do you use synthetic division to divide #( x^4 - 2x^3 + x - 8 ) / ( x - 1 )#?

##### 1 Answer

Long divide the coefficients to find:

#x^4-2x^3+x-8 = (x-1)(x^3-x^2-x) -8#

#(x^4-2x^3+x-8)/(x-1) = x^3-x^2-x - 8/(x-1)#

#### Explanation:

I like to lay it out similar to long division, but just writing the coefficients...

There are other possible layouts, but I find this easiest to work with (especially when the divisor is more complex than linear).

Notice the

So write the dividend

Choose the first term

Write down the product of the first term of the quotient and the divisor under the dividend and subtract it, resulting in a remainder

Bring down the next term

Choose the next term

Continue in similar fashion until we run out of terms to bring down from the dividend.

At this point we arrive at a final quotient

So:

#x^4-2x^3+x-8 = (x-1)(x^3-x^2-x) -8#

or if you prefer:

#(x^4-2x^3+x-8)/(x-1) = x^3-x^2-x - 8/(x-1)#