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Final: Every Root

Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 48 of 51.

Find every real root of the cubic equation on the board. A cubic has at most three, and this one has all three.

Challenge

Solve ${x}^{3}-5{x}^{2}-x+5 = 0$ . Find every root.

Try it yourself

x^{3}-5x^{2}-x+5 = 0

Get $x$ alone

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Polynomials & Rational Expressions

1Polynomial Long Division

How Long Division Works The Remainder Theorem A Missing Term Recap: Long Division

4Polynomial Equations

Common Factor First Grouping to Solve Fourth Powers Recap: Polynomial Equations

7Adding and Subtracting

Same Bottom Different Bottoms Subtracting Factor the Bottoms First Recap: Adding Fractions

10Variation

Direct Variation Inverse Variation Work Together Recap: Variation

2Remainders and Factors

The Factor Theorem Finding a Missing Number Using a Known Factor Recap: Remainders and Factors

5Sign Charts

Between the Roots Outside the Roots A Negative Leading Term Reading a Sign Chart Recap: Sign Charts

8Rational Equations

Clearing Fractions x in the Bottom Cross-Multiplying A False Answer One True, One False Recap: Rational Equations

11Final Challenges

Final: Divide It OutFinal: Every RootFinal: One Fraction Final: Check the Answer Final: The Sign Chart

3Factoring Higher Degree

Factor by Grouping Grouping All the Way Difference of Cubes Sum of Cubes A Quadratic in Disguise Recap: Factoring

6Rational Expressions

Cancelling Factors Excluded Values Multiplying Dividing Recap: Rational Expressions

9Rational Inequalities

Signs of a Fraction Including the Edge Recap: Rational Inequalities