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Solving polynomial inequalities using a graph and algebraic methods.

A handwritten math worksheet titled "Solving Polynomial Inequalities" showing a graph of a polynomial function, step-by-step algebraic solutions, and the solution set in interval notation.

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Show Answer Key & Explanations Step-by-step solution for: Solving Polynomial Inequalities

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- Find the x-intercepts by setting y = 0 and solving the equation x³ + x² - 9x - 9 = 0, which factors to (x + 3)(x - 3)(x + 1) = 0, giving x = -3, -1, 3.
- Find the y-intercept by setting x = 0, yielding y = -9.
- Determine the end behavior: since the leading coefficient is positive and the degree is odd, the graph starts in Quadrant III and ends in Quadrant I.
- Identify the intervals where the function values are greater than zero by examining the graph: the function is above the x-axis for -3 < x < -1 and x > 3.
- Express the solution in interval notation: x ∈ (-3, -1) ∪ (3, ∞).

Parent Tip: Review the logic above to help your child master the concept of polynomial inequalities worksheet.

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