MAT 171 Unit 4 Review 2 Polynomial Inequalities Flashcard

Front

Solve the inequality: $ x^2 + 7x \geq 0 $.

Back

(-\infty, 0] ∪ [7, ∞)

Front

Solve the inequality: $ x^3 > 9x^2 $.

Back

(-\infty, 0) or (9, ∞)

Front

Solve the inequality: $ x^2 - 3x - 4 < 0 $.

Back

(-1, 4)

Front

Solve the inequality: $ x^2 - 5x + 4 \ge 0 $.

Back

(-\infty, 1] ∪ [4, ∞)

Front

Solve the Polynomial Inequality: (x + 3)(x - 7) ≤ 0.

Back

[-3, 7]

Front

What is a polynomial inequality?

Back

An inequality that involves a polynomial expression, such as $p(x) \geq 0$ or $p(x) < 0$.

Front

What is the first step in solving polynomial inequalities?

Back

Factor the polynomial if possible.

Front

What does the solution set of a polynomial inequality represent?

Back

The set of x-values for which the polynomial is either greater than or less than zero.

Front

How do you determine the intervals for testing in polynomial inequalities?

Back

Identify the roots of the polynomial and use them to divide the number line into intervals.

Front

What is the significance of the roots in polynomial inequalities?

Back

Roots are the x-values where the polynomial equals zero and are critical points for testing intervals.