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

The correct option is B.

Explanation:

Answer 2

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+ √(2)`, so lets set
`1+ √(2)` equal to
`x` and factor backwards:

`x=1+ √(2)`

`x-1= √(2)`

`x-1- √(2)=0`

`(x-(1+ √(2))=0`
(
`(x-(1+ √(2) ))` is a factor of our polynomial.

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