Question

Is x+1 a factor of x^3-x^2-(3-√3)x +√3

Answer 1

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Let p(x) = x³-x²- (3-√3)x + √3

To check if x+1 is a factor of p(x), we need to check if p(-1) = 0

p(-1) = (-1)³ - (-1)² - (3-√3)(-1) + √3

       = -1 -1 + 3 - √3 + √3

       = -2+3

       = 1

Since p(-1) ≠ 0,

x+1 is not a factor of p(x)

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