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

Question

mathstudent55 · Answer

Unless there is more information given, such as the polynomial must have rational coefficients, this question cannot be answered.

mathstudent55 · Answer

No. sorry. I take that back. i misread it.

mathstudent55 · Answer

A polynomial function with roots, a, b, c, ... has factors (x - a), (x - b), (x - c), ...

anonymous · Answer

There are answer choices, do you want me to send them too?

mathstudent55 · Answer

In other words, x minus each root is a factor.

mathstudent55 · Answer

Since the roots are $1 + \sqrt 2$ and -3, x minus each of those is a factor.

mathstudent55 · Answer

Yes, what are the choices?

anonymous · Answer

One moment.

mathstudent55 · Answer

ok

anonymous · Answer

attachment

anonymous · Answer

Did it send?

mathstudent55 · Answer

Ok.
Notice the roots you are given.
Let's look at $1 + \sqrt 2$.
One factor is x minus that square root.
That would be $x - (1 + \sqrt 2) $
This does not look like any of the choices, but we can work a little on it.
Let's distribute the negative outside the parentheses.
$x - (1 + \sqrt 2)$

$= x - 1 - \sqrt 2$

This is still not like any choice.
Does it mention anywhere in the section where this problem comes from that the polynomials must have rational coefficients?

anonymous · Answer

No, it just polynomial with real roots. It does not give any other details in the question.