Solving polynomial inequalities
Solve a factored polynomial inequality using a sign chart / test-interval analysis. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Solve the inequality.
−(x + 5)(x - 2) > 0
- x > 2 or x < −5
- −5 < x < 2
- x > 2
- all real x
Answer: -5 < x < 2
See one solved, step by step
Solve the inequality.
(x + 4)(x + 2)(x - 5) < 0
- all real x
- −2 < x < 5 or x < −4
- x < 5
- x > 5 or −4 < x < −2
📘 Worked solution
1Roots (zeros): x = −4, −2, 5. These split the number line into 4 intervals.The expression can only change sign at a root.
2Testing x = 6 (to the right of every root): ((6) + 4)((6) + 2)((6) - 5) > 0.The sign of the rightmost interval matches the sign of the leading coefficient (positive here).
3The sign alternates in each interval moving left across a root.Each root is a simple (single) zero, so the expression changes sign every time you cross one.
4−2 < x < 5 or x < −4Collect the interval(s) where the expression is negative.
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