Concept:Long division of a polynomial by a quadratic gives the remainder directly. The remainder has degree less than the divisor.Explanation:Divide 6x3+2x2−5x+1 by x2−x−1.First term: 6x×(x2−x−1)=6x3−6x2−6x.Subtract: (6x3+2x2−5x+1)−(6x3−6x2−6x)=8x2+x+1.Next term: 8×(x2−x−1)=8x2−8x−8.Subtract: (8x2+x+1)−(8x2−8x−8)=9x+9.Since the degree of 9x+9 is less than the degree of x2−x−1, division stops.So the quotient is 6x+8 and the remainder is 9x+9.
