Yeah it looks all right to me.
Please check my answers.
1. Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.
(x - 3)(x + 2) > 0
This is what I did:
x-3=0 or x+2=0
x=3 or x=-2
The graph (-∞, -2) u (3, ∞)
2. x^2-6x+5 > 0
This is what I did:
I factor it: x^2-1x-5x+5
x(x-1) - 5(x-1)
(x-1)(x-5)
x=1 x=5
The graph: (-∞, 1) u (5, ∞)
3.x^2-3x-18<0
This is what I did:
I factor it: x^2+3x-6x-18
x(x+3) -6(x+3)
(x+3)(x-6)=0
x=-3 or x=6
The graph: (-∞, -3) u (6, ∞)
4.x^2-3x-28 < or equal to 0
This is what I did:
I factor it: x^2+4x-7x-28
x(x+4) -7(x+4)
(x+4)(x-7)
x=-4 x=7
The graph (-∞, -4] u [7, ∞)
5. x^2-4x < or equal to -3
this is what I did:
I added 3 to both sides, then got x^2-4x+3 < or equal to 0
factor it: x^2-1x-3x+3
x(x-1) -3(x-1)
(x-1)(x-3)=0
x=1 x=3
this is the graph: (-∞, -3] u[-1, ∞)