For the following exercises, solve the equation by...

For the following exercises, solve the equation by factoring. You will need to set the equation equal to 0 first, then find the greatest common factor, and finally see if further factoring is possible.
$x^3+5 x^2=-4 x$

Key Concepts

Polynomial Equations

A polynomial equation involves expressions composed of variables and coefficients with operations of addition, subtraction, multiplication, and non-negative integer exponents. Understanding these equations is essential because many problems throughout algebra, calculus, and applied mathematics require finding the values that satisfy these equations.

Setting Equations Equal to Zero

This technique involves rearranging the equation so that one side is zero. It is a critical first step in many methods of solving equations, as it allows for the use of properties like the Zero Product Property, which is applicable when the equation is expressed as a product of factors equal to zero.

Greatest Common Factor (GCF)

The greatest common factor is the largest expression that divides two or more terms in an algebraic expression without leaving a remainder. Factoring out the GCF simplifies the expression and can make subsequent factoring steps more apparent and manageable.

Factoring Techniques

Factoring is a method used to simplify polynomial expressions by breaking them down into products of simpler expressions, or factors. This technique is essential in solving equations because it allows for the application of the zero product property to identify the roots of the equation.

Zero Product Property

The Zero Product Property states that if a product of two or more factors is equal to zero, then at least one of the factors must be zero. This property is a fundamental tool in solving equations that have been factored, as it breaks down the equation into simpler, solvable parts.

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