How do you long divide #(3x^5 + 8x^4 - 2x^3 + x^2 +3x + 6) / (3x^2 + x +4)#?
1 Answer
#(3x^5+8x^4-2x^3+x^2+3x+6)/(3x^2+x+4)#
#=x^3+7/3x^2-25/9x-50/27+(431/27x+362/27)/(3x^2+x+4)#
Explanation:
You can long divide these polynomials like this...
The process is similar to long division of numbers.
Write the dividend (
Choose the first term
Write the product of this first term of the quotient and the divisor under the dividend. and subtract it to give a running remainder.
Bring down the next term
Choose the next term
Write the product of this term and the divisor under the running remainder and subtract it, etc.
Repeat until the running remainder is shorter than the divisor.
In this example we find that the quotient is:
#x^3+7/3x^2-25/9x-50/27#
with remainder:
#431/27x+362/27#