Question

How to do this question?

Answer 1

See below

Explanation:

Rational root theorem states that rational roots of a polynomial will take the form of `p/q` where `p` is a factor of the constant term and `q` is a factor of the leading coefficient. So, for `f(x)=12x^3+20x^2-x-6`

`p={1,2,3,6}`
`q={1,2,3,4,6,12}`

`p/q={+-1,+-1/2,+-1/3,+-1/4,+-1/6,+-1/12,+-2,+-2/3,+-3,+-3/2,+-3/4,+-6}` (take each value of p and divide it by each and every value of q)

Now, theoretically, we would test each of these `p/q` values to find which ones are actually zeros of the function `f(x)=12x^3+20x^2-x-6`

Truthfully, what you can do is find the rational zeros in your calculator and prove that they are zeros by using traditional or synthetic substitution. Once you know a root, the factor is `(x-a)` where `a` is your root.