SOLUTION: please help me solve this equation in interval notation x^3+5x<6x^2 I tried moving it to one side and did synthetic division which gave me x(x-5) and then I did the sign diagr

x^3 + 5x < 6x^2  ====>

x^3 - 6x^2 + 5x < 0  ====>  factor left side  ====>

x*(x^2 -6x + 5) < 0  ====>  factor the quadratic polynomial  ====>

x*(x-5)*(x-1) < 0.


There are 3 critical points - the roots of the polynomial, where is becomes eqial to zero:

x = 0,  x = 1   and x = 5,

and there are 4 intervals:

(-infinity,0), where the function is NEGATIVE;

(0,1), where the function is positive;

(1,5), where the function is negative;  and

(5,infinity), where the function is positive.


Now YOU make an effort and complete the solution.