Question

When x³ − 2x² + ax − b is divided by x² − 2x − 3, the remainder is x − 6. The values of a and b are respectively

(a) −2, −6

(b) 2 and −6

(c) −2 and 6

(d) 2 and 6

Answer 1

If the reminder (x −6) is subtracted from the given polynomial then rest of part of this polynomial is exactly divisible by x² − 2x − 3.

Therefore,

Now,

Therefore, are factors of polynomial p(x).

Now,

And

and

Solving (i) and (ii) we get

Hence, the correct option is (c).