Answer :

Let p(x) = 2x3 +3x2 + ax + b


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)


p(2) = 2(2)3 +3(2)2 + a(2) + b


p(2) = 16 + 12 + 2a + b


Also, it is given that p(2) = 2, on substituting value above, wev get,


2 = 28 + 2a + b


2a + b = –26 ---------- (A)


Similarly,


Remainder of p(x) when divided by x + 2 is p(–2)


p(–2) = 2(–2)3 +3(–2)2 + a(–2) + b


p(–2) = –16 + 12 – 2a + b


Also, it is given that p(–2) = –2, on substituting value above, we get,


–2 = –4 – 2a + b


– 2a + b = 2 ---------- (B)


On solving the above two equ. (A) and (b), we get,


a = –7 and b = –12


Value of a and b is –7 and –12 respectively.


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