Can you please help me with these math factoring!!?

Question

number 1 is less than or equal to!! i have to solve these algabraically

1. x^3 - 3x + 1 < 0

2. x^2 (3+x)(x+4)

------------------------------ > 0

(x+5)(x-1)

3. x^2 - 5x + 3

---------------------------- < 0

x-5

Answer 1

1. x^3 - 3x + 1 &lt; 0  

x(x^2-3)&lt;-1  since it&#039;s &lt;-1, x or x^2-3 has to be &lt; 0, but not both

x=1 or x &lt;-2

2.

x^2 (3+x)(x+4)/(x+5)(x-1)&gt;0

This isn&#039;t algebraically, but for this, x cannot = -3, -4, -5, 0 or 1 or either the numerator or denominator would be 0 and not &gt; 0.

-5&gt;x&gt;1

3.

x^2 - 5x + 3/x-5&lt;0

In order for it to be &lt;0, x-5&lt;0, x&lt;0 or x(x-5)&lt;-3 so

x&lt;5, x&lt;0, x&lt;0 or x-5&lt;0 so x&lt;5.

Sorry, I don&#039;t know of any other way to do these.