Polynomial Inequalities:
4) x^2 + 8x > 0
show your number line test and state answer in interval notation
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)"
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