Question

Question #463b6

Answer 1

`x>6 or 2>x>(-6)`

Explanation:

If you multiply the brackets you will get `x^3` as the largest exponent. Therefore, it will get large values if you insert large values. Also it will get large negative values if you insert large negative values. Because it has the zeropoints at `x_1=-6`, `x_2=2` and `x_3=6`, the graph is going to be above the x-axis for `x>6` as well as `2>x>(-6)`
graph{(x-6)(x-2)(x+6) [-20.24, 22.39, -5.94, 15.35]}

Answer 2

(-6,2) U (6, `+oo`)

Explanation:

Non-graphical method of solving these types of inequalities is given below:

Let p(x) denote (x+6)(x-2)(x-6). Divide the entire domain in four intervals `(-oo, -6); (-6,2); (2,6) and (6,oo)` Now consider any test value in these intervals and for each of these, note down the sign of each of the factor (x+6) (x-2) and (2,6) and the sign of p(x) The interval which returns the sign of p(x) > 0, is the required answer. Illustrative chart is given below: