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Question
In the following two polynomials, find the value of a, if x − a is factor x6 − ax5 + x4 − ax3 + 3x − a + 2.
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Solution
Let `f(x) = x^6 - ax^5 + x^4 - ax^3 + 3x - a + 2` be the given polynomial.
By factor theorem, (x − a) is a factor of the polynomial if f(a) = 0
Therefore,
`f(a) = a^6 -a(a)^5 + (a)^4 + (a)^4 - a(a)^3 + 3(a) - a + 2 = 0`
`a^6 - a^6 + 4^4 - a^4 + 2a + 2 = 0`
`2a + 2 = 0`
`a=-1`
Thus, the value of a is − 1.
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