Question

Factor each trinomial completely. $$ a^{2}-10 a-24 $$

   Factor each trinomial completely.
$$ a^{2}-10 a-24 $$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 13, Problem 65

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Solved by Expert Victor Salazar

04/05/2022

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Those numbers are -12 and 2. Show more…

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Factor each trinomial completely. $$ a^{2}-10 a-24 $$

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Key Concepts

Quadratic Expressions

Quadratic expressions are second-degree polynomials typically written in the form ax² + bx + c. They form the basis of many algebraic problems and are integral to understanding concepts like parabolic graphs, roots of equations, and the behavior of functions. Mastery of quadratic expressions is essential for solving equations systematically and for further studies in algebra.

Factoring Trinomials

Factoring trinomials involves rewriting a quadratic expression as a product of two binomials. This process simplifies solving equations by breaking down the quadratic into simpler components. The key to factoring is to find two numbers that multiply to the product of the quadratic coefficient and the constant term, while also adding to the linear coefficient, which then allows the expression to be split and factored by grouping.

Product-Sum Method

The product-sum method is a systematic approach to factor quadratic expressions. This technique involves finding a pair of numbers whose product equals the product of the leading coefficient and the constant term, and whose sum equals the middle coefficient. Once these numbers are determined, the quadratic can be split and factored, making the method a powerful tool for efficiently handling a wide range of quadratic expressions.

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