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A Negative Product

Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 16 of 63.

The machine survives minus signs; it just hunts among negative numbers too. x^2 + 2x - 8: the product must be -8, and a negative product means the pair has OPPOSITE signs, one plus and one minus.

Hunt pairs of 8 and give one of each pair a minus, aiming the sum at +2: 4 - 2 = 2 works, so the pair is 4 and -2, and x^2 + 2x - 8 = (x + 4)(x - 2). Writing x - 2 for adding -2 is the same shorthand as always.

The sign of c is the machine's first question from now on. Negative c: opposite signs, and the middle decides which of the pair carries the minus. Positive c: same signs, next lessons. Read c before hunting and half the candidates vanish.

Challenge

Easy

Factor x^2 + 3x - 10. The constant's sign narrows the hunt.

Try it yourself

x^2 + 3x - 10

Factor the expression

Test yourself

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

All lessons in Factoring & Quadratics

1What Factoring Is

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

4Minus Signs in the Machine

A Negative ProductWhich 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 One Higher Powers Three Terms Share Too Recap: 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