How do you divide #(4x^3 + 2x^2 + 9x)/(x^2+2x+1)#?
1 Answer
Apr 1, 2016
#(4x^3+2x^2+9x)/(x^2+2x+1)=4x-6 + (17x+6)/(x^2+2x+1)#
Explanation:
It is possible to long divide the polynomials or simply their coefficients, but let's just pick out the quotient and remainder step by step:
#(4x^3+2x^2+9x)/(x^2+2x+1)#
#=(4x^3+8x^2+4x-6x^2+5x)/(x^2+2x+1)#
#=(4x(x^2+2x+1)-6x^2+5x)/(x^2+2x+1)#
#=4x+(-6x^2-12x-6+17x+6)/(x^2+2x+1)#
#=4x+(-6(x^2+2x+1)+17x+6)/(x^2+2x+1)#
#=4x-6 + (17x+6)/(x^2+2x+1)#
