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Key Terms Chapter 07: Factoring

Last updated

Apr 2, 2025
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- Key Terms Chapter 06: Polynomials
- Key Terms Chapter 08: Rational Expressions and Equations Introductions

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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,
$\begin{matrix} (Key Terms Chapter 07.1) & a^{2} + 2 a b + b^{2} = {(a + b)}^{2} a^{2} - 2 a b + b^{2} = {(a - b)}^{2} \end{matrix}$

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

$\begin{matrix} (Key Terms Chapter 07.2) & a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2}) \end{matrix}$

$\begin{matrix} (Key Terms Chapter 07.3) & a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}) \end{matrix}$

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.