Question

If a polynomial function f(x) has roots 1+square root of 2 and-3, what must be a factor of f(x)?

Answer 1

To find the factor a a polynomial from its roots, we are going to seat each one of the roots equal to$x$, and then we are going to factor backwards.

We know for our problem that one of the roots of our polynomial is -3, so lets set -3 equal to$x$ and factor backwards:
$x=-3$
$x+3=0$
$(x+3)$ is a factor of our polynomial.

We also know that another root of our polynomial is $1+ \sqrt{2}$, so lets set $1+ \sqrt{2}$ equal to $x$ and factor backwards:
$x=1+ \sqrt{2}$
$x-1= \sqrt{2}$
$x-1- \sqrt{2}=0$
$(x-(1+ \sqrt{2})=0$
($(x-(1+ \sqrt{2} ))$ is a factor of our polynomial.

We can conclude that there is no correct answer in your given choices.