Please Help ASAP!!!

Question

Analyze the following polynomial function showing all your work: 

 

f(x) = x^4−x^3+7x^2−9x −18

 

 

Using this function (and the equivalent equation where f(x)=0) perform the 5 steps listed below and show all your work for each step. There are 3 points for each step including showing all your work for each step. 

 

For three points each answer the following questions showing all your work: 

 

1. What are all the possible rational roots (if any) for the equation? (Show all your work.) 

 

1. Use Synthetic Division to find actual roots from the list above. Start with the roots that are closest to the origin (smallest absolute value). Start each new trial divisor using the previous resulting depressed polynomial.  Show ALL Your Work! 

 

 

1. Use the resulting 2nd degree depressed polynomial to state the remaining Quadratic equation in Standard Quadratic Trinomial equation form. 

[Equation] 

1. Solve this Quadratic showing all your work. State the solutions in simplified form. 
2. Graph the original 4th degree polynomial function either manually or using technology (Desmos). Clearly show all x- and y-intercepts by labeling them with the their coordinates.   

Answer 1

roots -1, 2

found by graphing

divide 4d poly by x+1 and x-2

then use quadratic formula for other 2 roots