Question

Factor each expression. $$ x^{2}-5 x-14 $$

   Factor each expression.
$$
x^{2}-5 x-14
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 19

Instant Answer

Solved by Expert Robert Leedy

01/17/2020

Step 1

Here, the coefficient of $x^2$ (a) is 1, the coefficient of $x$ (b) is -5, and the constant term (c) is -14. Show more…

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Factor each expression. $$ x^{2}-5 x-14 $$

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Key Concepts

Quadratic Expression Factoring

This specific application of polynomial factoring involves quadratic expressions, which are polynomials of degree two. The goal is to express the quadratic as the product of two linear factors. This method is essential in solving quadratic equations and understanding the properties of parabolic functions.

Product-Sum Method

This is a common technique used in factoring quadratic expressions. It involves finding two numbers that multiply to give the product of the coefficient of the quadratic term and the constant term, and that add to give the coefficient of the linear term. This method provides a systematic approach to breaking down the quadratic into two binomial factors.

Polynomial Factoring

This is the process of rewriting a polynomial as a product of simpler polynomials. It is a fundamental algebraic technique used to simplify expressions and solve equations by breaking a complex expression into factors that, when multiplied together, yield the original polynomial.

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