Higher Powers

Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 7 of 61.

${x}^{5}+{x}^{3} = {x}^{3}\left({x}^{2}+1\right)$

Only three $x$ 's go in front, because ${x}^{3}$ has only three. Take out the smallest power. The 1 stays, because $\frac{{x}^{3}}{{x}^{3}}$ is 1. With three terms, the factor must divide all three.

Challenge

Factor $2{x}^{4}+6{x}^{3}+2{x}^{2}$ completely.

Try it yourself

2x^{4}+6x^{3}+2x^{2}

Factor

All lessons in Factoring & Quadratics

1What Factoring Is

Two Directions The Reverse Gear Un-Distributing Letters Recap: First Factors

4Minus Signs in the Machine

A Negative Product Which One Gets the Minus Both Negative The Sign Map Recap: Signs

7The Zero Product Rule

A Product That Makes Zero One Factor Is Enough The Bare X Every Factor Gets a Turn Recap: Zero Product

10The Quadratic Formula

The Formula, Stated The Number Under the Root Split the Plus-Minus It Always Works Choosing a Method Recap: The Formula

2The Greatest Common Factor

Number and Letter Together The Largest OneHigher PowersRecap: The GCF

5Special Shapes

A Missing Middle The Shape in Letters The Perfect Square The Minus Version Prime Polynomials Recap: Special Shapes

8Solving by Factoring

Factor, Then Split Signs Under Pressure Arrange It First The GCF Route Bigger Fronts Recap: Solve by Factoring

11How Many Solutions?

Two, One, or None The Double Root None at All Recap: Counting Solutions

3The Sum-Product Machine

Reading the Product Hunting the Pair The Machine in Letters Longer Hunts Recap: The Machine

6Factor Completely

Two Layers Squares Inside Completely Means Completely The Deep Check Recap: Factor Completely

9The Square Root Method

Undoing a Square Arrange, Then Root A Squared Package Roots That Are Not Whole Recap: Square Roots

12Final Challenges

Final: The Full Sweep Final: Factor and Split Final: Arrange First Final: The Rug, Modeled Final: The Rug, Solved Final: No Training Wheels