Question

Solve polynomial inequality and graph solution set on a real number line. x^3-7x^2-x-7<0

this is what I have so far,
(x+7)(x^2-1)=0
(x+7)(x-1)(x+1)=0
x+7=0, x-1=0, x+1=0
x=-7, x=1, x=-1

how do I know what side of the number line to shade?

Answer 1

I'm going to assume that your factors are correct (they do look OK).

Graph these three x-values on a horizontal number line.

Draw in the sets of x-values defined by these 3 x-values on the number line. For example, between -1 and 1 you have