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Question
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
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Solution
Let polynomial
P(x) = 3x3 + x2 – ax – 81
x – a is a factor of P(x)
Then putting x – a = 0
i.e. x = a in P(x) we get
P(a) = 0
3a3 + a2 – a × a – 81 = 0
3a3 = 81
a3 = 27
`\implies` a = (27)1/3 = 3
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