Solve the Polynomial Inequality College Algebra MyMathlab Homework

TL;DR

Learn how to solve polynomial inequalities and plot the solution set on a number line using the test point method.

Transcript

solve the polynomial inequality and graph the solution set on a real number line so we have X minus 2 times X plus 7 X minus 2 times X plus seven less than or equal to zero so to solve inequalities we use something called the test point method so the first step I guess is to factor but that's already done for us then we set each piece equal to zero... Read More

Key Insights

• 😥 The test point method is a useful strategy for solving polynomial inequalities.
• 🧑‍🏭 Factoring the polynomial is the first step in solving the inequality.
• 🫥 Plotting the solutions on a number line helps visualize the solution set.
• 😥 Choosing test points and checking their truth value helps determine the shaded regions.

Questions & Answers

Q: How do you solve a polynomial inequality using the test point method?

To solve a polynomial inequality, first factor the polynomial and set each factor equal to zero. Then, plot the solutions on a number line. Choose test points, such as zero, and plug them into the inequality to determine which regions to shade.

Q: What happens if the test point is true for the inequality?

If the test point is true for the inequality, you shade the region where the test point is located on the number line. This means that the test point satisfies the inequality and is part of the solution set.

Q: What if the test point is false for the inequality?

If the test point is false for the inequality, you shade the regions on the number line that are not where the test point is located. This means that the test point does not satisfy the inequality and is not part of the solution set.

Q: How do you determine the type of brackets to use in the final answer?

If the inequality is of the form "less than or equal to" or "greater than or equal to," use brackets in the final answer. If the inequality is only "less than" or "greater than," use parentheses.

Summary & Key Takeaways

• To solve the polynomial inequality, factor the polynomial and set each factor equal to zero.

• Plot the solutions on a number line and choose test points to check if the inequality is true.

• Shade the regions on the number line based on the test point results and determine the type of brackets to use in the final answer.