when x^3-2x^2+ax-b is divided by x 2 −2x−3, the remainder is x−6. The values of a and b are respectively -2 and 6
x3−2x2+ax−b is divided by x2−2x−3 and the remainder obtained is x−6.
Now, the first term in the quotient will be x since the coefficient of x3 is 1.
So, x(x2−2x−3)=x3−2x2−3x, which when subtracted from the dividend gives (a+3)x−b
Since the degree of the above term is less than the divisor, it is the remainder and so we equate it to x−6
Hence, a+3=1 and b=6
⇒a=−2,b=6
