Question

${x} ^3 - {x}^2 - (3 - \sqrt{3} )x + \sqrt{3}$
is this polynomial has (x+1) as a factor ​

Answer 1

Answer:

${x}^{3} - {x}^{2} - (3 - \sqrt{3} )x + \sqrt{3} \\ = - 1 - 1 + 3 - \sqrt{3} + \sqrt{3} \\ 1$

No (x+1) is not a factor of the polynomial.

Answer 2

Step-by-step explanation:

Given polynomial is p(x)=x³-x²-(3-√3)x+√3

given another polynomial is (x+1)

we know that by factor theorem

a polynomial (x+a) is a factor of p(x) if p(x)=0

=>If (x+1) is a factor then p(-1)=0

=>p(-1)=(-1)³-(-1)²-(3-√3)(-1)+√3

=>-1-1+3-√3+√3

=>-2+3+0

=>1

p(-1)=1

So (x+1) is not a factor of x³-x²-(3-√3)x+√3