# How do you find all the zeros of #f(x) = x^3 – 3x^2 – 16x + 48#?

##### 1 Answer

May 11, 2016

i.e. zeros are at

#### Explanation:

Note that a polynomial of degree 3 (such as this one) should have 3 zeroes (although there is no way to be sure that they will all be unique or Real).

There are multiple ways to analyze this but I chose the way that required the least thinking on my part.

Hoping for at least one rational (in this case, integer) zero

I applied the Factor Theorem to all integer factors of

and (using a spreadsheet for the donkey work) got:

This worked even better that I had hoped.

As you can see this gives me all 3 zeros!