How would I solve this inequality and graph?

(x+2)((x^(2)-x+1)) > 0

I got x > -2 and x^(2)-x+1 > 0

How would I graph x^(2)-x+1 > 0
because I can't factor it.

Would I just graph x>-2

I understand this now

To solve the given inequality, you correctly found that x > -2 is one of the solutions. Now, let's focus on solving x^2 - x + 1 > 0.

Since you mentioned that factoring the quadratic equation is not possible, we can resort to another method to determine the solution set. One approach is to use the concept of the discriminant. The discriminant (Δ) of a quadratic equation ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac.

For the equation x^2 - x + 1 = 0, the coefficients are a = 1, b = -1, and c = 1. So, the discriminant is Δ = (-1)^2 - 4(1)(1) = 1 - 4 = -3.

Since the discriminant is negative (Δ < 0), there are no real solutions to the equation x^2 - x + 1 = 0. This means that the quadratic equation x^2 - x + 1 is always positive and does not cross the x-axis.

Therefore, the solution to x^2 - x + 1 > 0 is all real numbers.

To graph this inequality, you can follow these steps:

1. Draw a number line.
2. Mark the point -2 on the number line.
3. Since the inequality is x > -2, shade the number line to the right of -2 to represent all values greater than -2.
4. Since the solution set is all real numbers for x^2 - x + 1 > 0, the entire number line should be shaded.
5. Indicate that the circle at -2 on the number line is open (since x > -2 and not x ≥ -2).

The resulting graph represents the solution to the inequality (x + 2)((x^2 - x + 1)) > 0.