Question

Determine whether x cube minus x square minus [3+ root 3 minus] x minus root 3 has(x minus 1) has a factor

Answer 1

Given function is $f(x)=x^3-x^2-(3+\sqrt{3})-x-\sqrt{3}$

Now we have to check if (x-1) is it's factor or not.

To check that we simply plug x=1 into given function to see if it produces 0 or not. Notice that x=1 is obtained from (x-1). we just take opposite sign.

now let's plug x=1 into given function.

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

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

$f(1)=1-1-(3+\sqrt{3})-1-\sqrt{3}$

$f(1)=-3-\sqrt{3}-1-\sqrt{3}$

$f(1)=-4-2\sqrt{3}$

Which is never going to become 0 in any way.

Hence (x-1) is NOT the factor of given function.

Given function was hard to read so i made up equation as per my best understanding. If you feel that equation is not correct then you can repeat same process with correct equation to get the answer.