Question

The inequality x2 − 9 x2 + 6x + 8 > 0 can be factored as: (x + 3)(x - 3) (x + 4)(x + 2) > 0 Use the critical points to determine the test regions. Which are possible test points? –5 –4 –3.5 –3 –2.5 –2 0 5

Answer 1

The answers are:

-5

-3.5

-2.5

0

5

Explanation:

Answer 2

The possible test points are -5,-3.5 , -2.5,0,5

Explanation:

Given : The inequality
`(x^2-9)/(x^2+6x+8)>0` can be factored as

(x + 3)(x - 3) (x + 4)(x + 2) > 0

To find : Which are possible test points?

Solution : The inequality factored as

`(x^2-9)/(x^2+6x+8)>0`

`((x + 3)(x - 3))/((x + 4)(x + 2))>0`

The critical points are defined as when we equation the factor to zero then the value of x is the critical point.

So, x+3=0 ⇒ x=-3

x-3=0 ⇒ x=3

x+4=0 ⇒ x=-4

x+2=0 ⇒ x=-2

The critical points of the given inequality are -4,-3,-2,3

The possible test points are the points except critical points.

Therefore, Out of the given options

The possible test points are -5,-3.5 , -2.5,0,5 as they are not critical points.