Question 1157549
factor out a -x(x^3-3x^2-13x)+15)=0
x=0 

synthetic division using -3


-3/ 1-----  -3 ------ -13 ----- 15
shown to be 1 ---  -6 ----- 5. which is x2-6x+5

so -3 is a root, and the trinomial factors into (x-5)(x-1)

roots are -3, 0, 1, and 5
factors are -x(x+3)(x-1)(x-5).


 go back to -x^4+3x^3+13x^2-15x
when x becomes very negative, < -3. so does the function
-3 < x < 0 will be positive

0< X < 1 will be negative 
1 < x < 5 will be positive
and for large + x >5 the function will be negative.




{{{graph(300,300,-5,7,-50,100,-x^4+3x^3+13x^2-15x)}}}