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Question
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
Solution
Let `f(x) = x^5 - a^2 x^3 + 2x + a `+1 be the given polynomial.
By factor theorem, (x − a) is a factor of f(x), if f(a) = 0.
Therefore,
`⇒ f(a) = (a)^5 - a^2(a)^3 + 2 (a) + a + 1 = 0`
`a^5 - a^5 + 2a + a+1 = 0`
`3a + 1 = 0`
` a= (-1)/3`
Thus, the value of a is − 1/3.
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