Multiple Choice
Solve the given equation by factoring.
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1. Equations & Inequalities
Intro to Quadratic Equations
2:01 minutesProblem 9
Textbook Question
Solve each equation in Exercises 1 - 14 by factoring.
Verified step by step guidance1
Start by writing the equation: \$3x^2 + 12x = 0$.
Factor out the greatest common factor (GCF) from both terms. The GCF of \$3x^2\( and \)12x\( is \)3x\(, so factor it out: \)3x(x + 4) = 0$.
Apply the Zero Product Property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero: \$3x = 0\( and \)x + 4 = 0$.
Solve each equation separately: For \$3x = 0\(, divide both sides by 3 to get \)x = 0\(. For \)x + 4 = 0\(, subtract 4 from both sides to get \)x = -4$.
Write the solution set combining both values: \(x = 0\) and \(x = -4\).
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring Quadratic Expressions
Factoring involves rewriting a quadratic expression as a product of simpler expressions, typically binomials or monomials. For example, 3x² + 12x can be factored by taking out the greatest common factor (GCF), which simplifies solving the equation.
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Greatest Common Factor (GCF)
The GCF is the largest expression that divides all terms of a polynomial without a remainder. Identifying and factoring out the GCF simplifies the equation, making it easier to solve by setting each factor equal to zero.
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Zero Product Property
This property states that if the product of two factors equals zero, then at least one of the factors must be zero. After factoring the equation, set each factor equal to zero to find the solutions of the equation.
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