How do you divide #(x^4 - 7x^3 + 2x^2 + 9x)/(x^3-x^2+2x+1)#?
Long divide the coefficients to find:
#(x^4-7x^3+2x^2+9x)/(x^3-x^2+2x+1) = x-6 + (-6x^2+4x+6)/(x^3-x^2+2x+1)#
That is, the quotient is
I like to long divide the coefficients, not forgetting to include
The process is similar to long division of numbers.
Write the dividend (
Choose the first term
Write out the product of this first term of the quotient and the divisor below the dividend and subtract it.
Bring down the next term (
Choose the next term
Write out the product of this second term of the quotient and the divisor below the remainder and subtract it.
The resulting remainder
In this example, we find the quotient is