The division algorithm says that result of division of the polynomial f(x) by another polynomial d(x) can be stated as f(x)=q(x)d(x)+r(x) where d(x),q(x), and r(x) are called divisor, quotient, remainder respectively. Carry out following divisions, by using either long division or synthetic division, and write the answers as f(x)=q(x)d(x)+r(x).
i) 3x^3-x^2-7 by x^2+1
ii) 6x^3+6x+9 by x-3
iii) -2x^3-x^2+5x-3 by x+2