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Mathematics LibreTexts

Key Terms Chapter 07: Factoring

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Difference of Squares Pattern
If a and b are real numbers,

This image shows the difference of two squares formula, a squared – b squared = (a – b)(a + b). Also, the squares are labeled, a squared and b squared. The difference is shown between the two terms. Finally, the factoring (a – b)(a + b) are labeled as conjugates.
Factoring
Factoring is splitting a product into factors; in other words, it is the reverse process of multiplying.
Greatest Common Factor
The greatest common factor is the largest expression that is a factor of two or more expressions is the greatest common factor (GCF).
Perfect Square Trinomials Pattern
If a and b are real numbers,

a2+2ab+b2=(a+b)2a22ab+b2=(ab)2

Prime Polynomials
Polynomials that cannot be factored are prime polynomials.
Quadratic Equations
are equations in which the variable is squared.
Sum and Difference of Cubes Pattern

a3+b3=(a+b)(a2ab+b2)

a3b3=(ab)(a2+ab+b2)

Zero Product Property
The Zero Product Property states that, if the product of two quantities is zero, at least one of the quantities is zero.

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