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Question
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
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Solution
The given polynomials are ax3 + 3x2 – 9 and 2x3 + 4x + a.
Let p(x) = ax3 + 3x2 – 9 and q(x) = 2x3 + 4x + a
Given that p(x) and q(x) leave the same remainder when divided by (x + 3),
Thus by Remainder Theorem, we have
p(–3) = q(–3)
`=>` a(–3)3 + 3(–3)2 – 9 = 2(–3)3 + 4(–3) + a
`=>` –27a + 27 – 9 = –54 – 12 + a
`=>` –27a + 18 = –66 + a
`=>` –27a – a = –66 – 18
`=>` –28a = –84
`=> a = 84/28`
∴ a = 3
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