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Question
If the polynomials ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.
Solution
Let p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 - 4x + a be the given polynomials.
When p(x) and q(x) are divided by (x - 3) the remainder are p(3) and q(3) respectively.
p(3) = q(3) given
a(3)3 + 4(3)2 + 3 x 3 - 4 = 33 - 4 x 3 + a
⇒ 27a + 36 + 9 - 4 = 27 - 12 + a
⇒ 26a = 15 - 41
⇒ 26a = -26
∴ a = `-(26)/(26)`
= -1.
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