If f(x)=3x^3+5x^2+x-1,what would be the p/q list of possible rational roots?
arrange your list from smallest to largest.

  {-1, -1/3, 1/3, 1}

Step-by-step explanation:

The possible rational roots are ...

  ±(divisor of constant)/(divisor of leading coefficient)

Here, that means the rational roots are ...

  ±p/q where p ∈ {1}, and q ∈ {1, 3}

That is, they can be ±1/1 or ±1/3. Arranged from smallest to largest, they are ...

  -1, -1/3, 1/3, 1

_____

A graph shows the roots to be -1 (multiplicity 2) and (+1/3). Then the function factors as ...

  f(x) = (3x -1)(x +1)²

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol