Kevin B. answered • 05/02/19

Former Teacher and Math Expert

Here's one way to solve (x+4)^{2}·(x-6) > 0:

**Step 1** Solve (x+4)^{2}·(x-6) = 0

Hopefully, solving (x+4)^{2}·(x-6) = 0 will not be difficult. Since the left-hand side of this equation is already factored, we just need to set each factor equal to zero and solve for x.

(x + 4)^{2} = 0 <---> x = -4

x - 6 = 0 <---> x = 6

**Step 2** With these two values x = -4 and x = 6, we divide the number line into three sections

Section 1: all values x < -4

Section 2: all values -4 < x < 6

Section 3: all values x > 6

**Step 3 ** We now choose one test value of x for each section. If that value satisfies the inequality (x+4)^{2}·(x-6) > 0, then that section is part of our solution. Keep in mind, ** any** value from that section will due.

Section 1: Let x = -5. Then (-5+4)^{2}(-5-6) = (1) (-11) is negative. **NOT A SOLUTION**

Section 2: Let x = 0. Then (0+4)^{2}(0-6) = (16)(-6) is negative. **NOT A SOLUTION**

Section 3: Let x = 7. Then (7+4)^{2}(7-6) = (11^{2})(1) is positive. **SOLUTION**

Therefore, our solution lies in Section 3, that is all values of x greater than 6, {x | x > 6}

Jackie V.

Thank you so much! This was major help!05/02/19