Solution:
It is given that is the factor of and leaves remainder 4, when divided by .Let, .
Find the value of x which satisfies the given polynomial.
Since is the factor of a given polynomial, it must satisfy the given polynomial.
⇒x+2=0
⇒x=-2
At x = -2, we get,
⇒
⇒
…...eq(i)
Given that leaves remainder 4, when divided by .
Therefore, by putting in ,leaves the remainder 4. Hence, .
⇒
⇒
⇒
⇒ ……eq(ii)
Solving eq(i) and eq(ii),
⇒eq(i)+eq(ii), we get,
⇒)+
⇒
⇒
Putting value of ‘a’ in eq(ii), we get,
⇒
⇒
Therefore, option 1 is correct.