Question

Check whether $x+1$ is a factor of $x^3-x^2-(2+\sqrt{2})x+\sqrt{2}$.

• A. True
• B. False

Answer 1

The correct option is B False

The zero of $x+1$ is $-1$
Let $p\left(x\right)=x^3-x^2-(2+\sqrt{2})x+\sqrt{2}$
Then, $p(-1)=(-1{)}^3-(-1{)}^2-(2+\sqrt{2})(-1)+\sqrt{2}$
$=-1-1+2+\sqrt{2}+\sqrt{2}=2\sqrt{2}$
Since, $p(-1)\ne 0$
Therefore, by Factor theorem, $x+1$ is not a factor of $x^3-x^2-(2+\sqrt{2})x+\sqrt{2}$