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Question
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
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Solution
Let f(x) = ax3 + 3x2 – 3
When f(x) is divided by (x – 4), remainder = f(4)
f(4) = a(4)3 + 3(4)2 – 3 = 64a + 45
Let g(x) = 2x3 – 5x + a
When g(x) is divided by (x – 4), remainder = g(4)
g(4) = 2(4)3 – 5(4) + a = a + 108
It is given that f(4) = g(4)
64a + 45 = a + 108
63a = 63
a = 1
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