Solution:
It is given that is the factor of and leaves remainder 4, when divided by .Let, .
Finding the value of x which satisfies the given polynomial,
Since is the factor of a given polynomial, therefore, it must satisfy the given polynomial.
At x = 2, we get,
⇒
⇒
⇒
⇒ …...eq(i)
We know that leaves remainder 3, when divided by .
Therefore, putting in leaves the remainder 3. Hence, .
⇒
⇒
……eq(ii)
Therefore, solving eq(i) and eq(ii),
⇒eq(ii)-eq(i), we get,
⇒
⇒
⇒
Putting value of ‘a’ in eq(ii), we get,
⇒
⇒
Hence, the value of .
Therefore, option 1 is correct.