Question

Solve the equation by factoring. $$ x^{2}+7 x+10=0 $$

   Solve the equation by factoring.
$$
x^{2}+7 x+10=0
$$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 10, Problem 24

Instant Answer

Solved by Expert Cory Kuzinski

04/20/2020

Step 1

We look for two numbers that multiply to 10 and add up to 7. The numbers 5 and 2 satisfy these conditions. So, we can write the equation as follows: $$ x^{2}+7 x+10=(x+5)(x+2)=0 $$ Show more…

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Solve the equation by factoring. $$ x^{2}+7 x+10=0 $$

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Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0. Understanding its structure is crucial since it determines the methods available for finding the roots, whether by factoring, completing the square, or using the quadratic formula.

Factoring

Factoring is the process of writing a polynomial as a product of simpler expressions. For quadratic equations, this involves identifying two numbers that multiply to give the constant term and add up to give the linear coefficient, thereby decomposing the quadratic into two binomial factors.

Zero Product Property

The zero product property states that if a product of two factors is zero, at least one of the factors must be zero. This concept is key in solving factored equations because it allows one to set each individual factor equal to zero to find the solutions of the equation.

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