# How do you find the zeros of the polynomial function with equation f(x) = x^3 +7x^2 - 4x - 28?

May 4, 2016

Using the Factor Theorem (hoping or integer factors) we find zeros at $x \in \left\{- 2 , + 2 , - 7\right\}$

#### Explanation:

According to the Factor Theorem if $\textcolor{b l u e}{1} {x}^{3} + 7 {x}^{2} - 4 x - \textcolor{red}{28}$ as rational zeros
they must be factors of $\frac{\textcolor{red}{28}}{\textcolor{b l u e}{1}}$

The possible factors are therefore
$\textcolor{w h i t e}{\text{XXX}} \left\{\pm 1 , \pm 2 , \pm 4 , \pm 7 , \pm 14 \pm 28\right\}$

Testing these factors:

we find three zeros (as given in the "Answer" above.

Since the given expression is of degree 3 and we have 3 zeros, these 3 zeros represent all possible solutions.