Question

please solve it fast

Answer 1

Given ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by x - 3.
 Let p(x) = ax3 + 4x2 + 3x - 4 and
g(x) = x3 - 4x + a 
By remainder theorem, if f(x) is divided by (x − a)
then the remainder is
f(a) Here when p(x) and g(x) are divided by (x − 3) the remainders are
p(3) and g(3) respectively.
 Also given that p(3) = g(3) 
→ (1) Put x = 3 in both p(x) and g(x) 
Hence equation (1) becomes,
a(3)3 + 4(3)2 + 3(3) - 4 = (3)3 - 4(3) + a 
⇒ 27a + 36 + 9 − 4 = 27 − 12 + a 
⇒ 27a + 41 = 15 + a 
⇒ 26a  = 15 − 41 = − 26
 ∴ a = −1

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