Answer :

Let p(x) = x3 + ax2 + 5 and q(x) = x3 – 2x2 + a


As we know by Remainder Theorem,


If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)


Remainder of p(x) when divided by x + 2 is p(–2). Similarly, Remainder of q(x) when divided by x + 2 is q(–2)


p(–2) = (–2)3 +a(–2)2 + 5


p(–2) = –8 + 4a + 5


p(–2) = –3 + 4a


Similarly, q(–2) = (–2)3 – 2(–2)2 + a


q(–2) = –8 –8 + a


q(–2) = –16 + a


Since they both leave the same remainder, so p(–2) = q(–2)


–3 + 4a = –16 + a


–13 = 3a



The value of a is –13/3


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