Write the function in factored form, and give all the possible rational zeros of the function.  

f(x) = x^4 − x^3 + 7x^2 − 9x − 18



Write the function in factored form, and give all the possible rational zeros of the function.  

f(x) = x^4 − x^3 + 7x^2 − 9x
**Answer:**



**Step-by-step explanation:Explanation:**


**First notice that by reversing the signs of the coefficients of the terms with odd degree, the sum is zero. So**


**x**


**=**


**−**


**1**


 **is a zero:**



**f**


**(**


**−**


**1**


**)**


**=**


**1**


**+**


**1**


**+**


**7**


**+**


**9**


**−**


**18**


**=**


**0**



**and**


**(**


**x**


**+**


**1**


**)**


 **is a factor:**



**x**


**4**


**−**


**x**


**3**


**+**


**7**


**x**


**2**


**−**


**9**


**x**


**−**


**18**



**=**


**(**


**x**


**+**


**1**


**)**


**(**


**x**


**3**


**−**


**2**


**x**


**2**


**+**


**9**


**x**


**−**


**18**


**)**



**then factor by grouping…**



**=**


**(**


**x**


**+**


**1**


**)**


**(**


**(**


**x**


**3**


**−**


**2**


**x**


**2**


**)**


**+**


**(**


**9**


**x**


**−**


**18**


**)**


**)**



**=**


**(**


**x**


**+**


**1**


**)**


**(**


**x**


**2**


**(**


**x**


**−**


**2**


**)**


**+**


**9**


**(**


**x**


**−**


**2**


**)**


**)**



**=**


**(**


**x**


**+**


**1**


**)**


**(**


**x**


**2**


**+**


**9**


**)**


**(**


**x**


**−**


**2**


**)**



**then take square root of**


**−**


**9**


 **to find:**



**=**


**(**


**x**


**+**


**1**


**)**


**(**


**x**


**−**


**3**


**i**


**)**


**(**


**x**


**+**


**3**


**i**


**)**


**(**


**x**


**−**


**2**


**)**



**So the zeros are**


**x**


**=**


**−**


**1**


**,**


**x**


**=**


**3**


**i**


**,**


**x**


**=**


**−**


**3**


**i**


 **and**


**x**


**=**


**2**


