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Question
If x − 2 is a factor of the following two polynomials, find the values of a in each case x5 − 3x4 − ax3 + 3ax2 + 2ax + 4.
Solution
Let f(x) = x5 − 3x4 − ax3 + 3ax2 + 2ax + 4 be the given polynomial.
By the factor theorem, (x − 2) is a factor of f(x), if f (2) = 0
Therefore,
`f(2) = (2)^3 - 3(2)^4 - a(2)^3 + 3a(2)^2 + 4 = 0 `
`32 - 48 - 8a + 12a + 4a + 4 = 0`
` - 12 + 8a = 0`
` a = 3/2`
Thus, the value of a is 3/2.
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