Answer to Question #236778 in Algebra for CCW

Question

Polynomial Inequalities:

4) x^2 + 8x > 0

show your number line test and state answer in interval notation

Answer 1

We may rewrite the inequality in form

$x(x+8) > 0.$

Next, we solve the equation

$x(x+8) = 0.$

The roots are equal to 0 and -8. We place these roots on the line and mark the sign of the left hand of the inequality.

At $(-\infty, -8)$ $x<0, x+8< 0 \; \Rightarrow x(x+8) >0,$

at $(-8,0)\;\; \;\;x<0, x+8> 0 \; \Rightarrow x(x+8) <0,$

at $(0,+\infty)\;\; \;\;x>0, x+8> 0 \; \Rightarrow x(x+8) >0,$

The answer will be $x\in(-\infty, -8) \cup (0,+\infty)$