How do you long divide #(x^4 + 2x^3 - x^2 - 2x + 4) /( x^2 + x - 1)#?
1 Answer
Explanation:
I prefer to long divide just the coefficients, which is basically the same process without writing the powers of
Note well that if there were any 'missing' powers of
The process is similar to long division of numbers:
Write the dividend under the bar and the divisor to the left.
Choose the first term
Write the product below the divisor and subtract.
Bring down the next term of the dividend alongside the difference and choose the next term
Repeat until the running remainder is shorter than the divisor.
We find that:
#(x^4+2x^3-x^2-2x+4)/(x^2+x-1) = x^2+x-1 + 3/(x^2+x-1)#