Consider the polynomial P(x)=3x5−4x4+2x3−7x2+x+5 and the divisor D(x)=x2−x+2.
(a) Find the quotient and the remainder obtained when P(x) is divided by D(x).
(b) Verify the division algorithm by showing that P(x)=D(x)(quotient)+(remainder) for all real values of x.