Question

What are all the possible rational zeros for `f(x)=5x^3-2x^2+20x-8`?

Answer 1

The possible rational zeros are: `+-1, +-2,+-4,+-8,+-1/5,+-2/5, +-4/5, +-8/5`

Explanation:

Find the possible rational zeros of:

`f(x)=color(red)5x^3-2x^2+2-x-color(blue)8`

The possible rational zeros are found by dividing the factors of the constant term `color(blue)8` (called `color(blue)p`) by the factors of the leading coefficient `color(red)5` (called `color(red)q`).

`color(blue)p/color(red)q=frac{+-1,2,4,8}{+-1,5}`

Dividing each number in the numerator by each number in the denominator gives:

`+-1, +-2,+-4,+-8,+-1/5,+-2/5, +-4/5, +-8/5`