Determine w

Let f(x) = x³ – x² – (3 –√3 ) x + √3

By Factor Theorem, we know that,

If p(x) is a polynomial and a is any real number, then (x – a) is a factor of p(x), if p(a) = 0

For checking (x+1) to be a factor, we will find f(–1)

⇒ f(–1) = (–1)³ – (–1)² – (3 –√3)(–1) + √3

⇒ f(–1) = –1 – 1 + 3 – √3 + √3

⇒ f(–1) = 1

As, f(–1) is not equal to zero, therefore (x+1) is not a factor x³ – x² –(3 –√3) x + √3