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.
$2 x^4=-30 x^3-88 x^2$

Key Concepts

Standard Form

Rewriting an equation in standard form involves setting the equation equal to zero. This allows for the use of various algebraic methods such as factoring because having zero on one side of the equation makes applying the zero product property straightforward. Establishing a common reference point with all terms on one side is a crucial first step in solving polynomial equations.

Greatest Common Factor (GCF)

The greatest common factor is the largest factor that is common to all terms in a polynomial. Identifying and factoring out the GCF from every term simplifies the equation and often reduces the degree of the polynomial, making subsequent factoring or solving more manageable.

Polynomial Factoring

Polynomial factoring is the process of breaking down a polynomial into a product of simpler expressions or factors. This step is vital for solving equations because, after factoring, each individual factor can be set equal to zero, applying the zero product property to solve for the variable.

Zero Product Property

The zero product property states that if the product of two or more factors is zero, then at least one of the factors must equal zero. This property is used to find the roots of a factored polynomial once the expression is written as a product of factors, allowing each factor to be set up as an equation to solve for the variable.

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