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Question
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
Solution
Let f(x) = x3 + ax2 − 2x +a + 4 be the given polynomial.
By the factor theorem, (+ a) is the factor of f(x), if f(− a) = 0, i.e.,
`f(-a) = (-a)^3 + a(-a)^2 -2(-a) + a + 4 = 0`
`-a^3 + a^3 2a + a + 4 = 0`
`3a + 4 = 0`
`a = (-4)/3`
Thus, the value of a is − 4/3.
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