Question

Solve each equation. $$ x^{3}-12 x^{2}+32 x=0 $$

   Solve each equation.
$$
x^{3}-12 x^{2}+32 x=0
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 6, Problem 57

Instant Answer

Solved by Expert Victor Salazar

02/09/2022

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This gives us: $$ x(x^{2}-12x+32)=0 $$ Show more…

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Solve each equation. $$ x^{3}-12 x^{2}+32 x=0 $$

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Key Concepts

Quadratic Equations

A quadratic equation is a specific type of polynomial equation of degree two. It often appears as a factor in more complex polynomial equations. Techniques for solving quadratic equations include factoring, using the quadratic formula, or completing the square. Understanding quadratic equations is a critical part of algebra, as they frequently emerge in various mathematical contexts and applications.

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 be zero. This principle is essential when solving factored equations because it provides a direct way to set each factor equal to zero and solve for the variable, thereby finding all possible solutions to the equation.

Factoring Techniques

Factoring is a method used to break down complex expressions into products of simpler expressions or factors. It simplifies polynomial equations by rewriting them as a product of simpler polynomials, making it easier to solve for the variable. This method can reveal hidden structures within equations, allowing for straightforward application of other algebraic properties, such as the zero product property.

Polynomial Equations

A polynomial equation is an equation that involves only sums, products, and non-negative integer exponents of a variable. Solving polynomial equations typically involves finding all values of the variable that satisfy the equation, and methods can include factoring, graphing, or using algebraic formulas. This concept is fundamental in algebra for understanding how expressions behave and finding their roots.

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