Question

Factor each expression. $$ x^{2}+x-12 $$

   Factor each expression.
$$
x^{2}+x-12
$$

Algebra 1 Common Core

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 10, Problem 58

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Solved by Expert Heather Zimmers

04/01/2020

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We need to factor this expression. Factoring is the process of breaking down an expression into a product of simpler expressions. Show more…

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Factor each expression. $$ x^{2}+x-12 $$

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Key Concepts

Quadratic Expression

A quadratic expression is a second-degree polynomial typically represented in the form ax² + bx + c. Its structure and properties, such as having a parabolic graph, make it fundamental in algebra. Analyzing quadratic expressions is essential for understanding the behavior of polynomial functions and finding their roots.

Factoring Quadratics

Factoring quadratics involves rewriting a quadratic expression as a product of two binomials. This process simplifies solving equations, graphing functions, and understanding the factors that make up the expression. The method often relies on identifying two numbers that multiply to the constant term and add up to the coefficient of the linear term.

Product-Sum Method

The product-sum method is a strategy used in factoring quadratic expressions. It requires finding two numbers whose product equals the constant term (or the product of the leading coefficient and the constant term in some cases) and whose sum equals the coefficient of the linear term. This approach provides a systematic way to break down and simplify the quadratic expression.

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