Also not sure on this, can you help

[jazzgirl]

(x+4)(x^2-9)>0

need to solve. I think I find what makes it zero so -4 and 9 but not sure of the steps.

 

[NRS]

-4 is correct, but remember, between the second set of parenthenthese, x is squared. This means that you have to find what would make 9 when squared, so that when you subtract 9 from it, it will be 0. The answer to this would be 3. because:

(3-4)(3^2-9)
= (-1)(9-9)
=(-1)(0) = 0

 

[wjm11]

(x+4)(x^2-9)>0

need to solve. I think I find what makes it zero so -4 and 9 but not sure of the steps.

You are on the right track. Notice that this inequality is a cubic (x has a power of 3 if you multiply it out). That means you may have up to three solutions for x when you set this equal to zero. The first step is to further factor the expression (x^2 – 9). This is the “difference of two squares” and factors as follows:

(x+4)(x^2-9) = 0
(x+4)(x – 3)(x + 3) = 0

Now set each individual factor equal to zero and solve:

x + 4 = 0
x = -4

x - 3 = 0
x = 3

x + 3 = 0
x = -3

If we graphed y = (x+4)(x – 3)(x + 3), we would see that the function crosses the x-axis at x = -4, -3, and 3.

To solve the inequality (your original problem), examine the regions around and in between these x values to see where the inequality is true. That means plug in an x value and see if the answer is greater than or less than zero. You need to identify the *regions* where the inequality is true.

 

[swaroop]

Solution goes this way:
x=4,-3,3 are critical points and x<-4,-3 and x>3
So solution is x<-4 and x>3