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Question
Determine the following polynomial has (x + 1) a factor:
`x^3-x^2-(2+sqrt2)x+sqrt2`
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Solution
If(x + 1) is a factor of polynomial `p(x) = x^3-x^2-(2+sqrt2)x+sqrt2`, then p(−1) must be zero, as a result (x + 1) is not a factor of this polynomial.
`p(-1) = (-1)^3 - (-1)^2 - (2+sqrt2)(-1) + sqrt2`
= `-1-1+2+sqrt2+sqrt2`
= `2sqrt2`
As p(−1) ≠ 0,
Therefore, (x + 1) is not a factor of this polynomial.
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