Here are the essential concepts you must grasp in order to answer the question correctly.
Factoring
Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In the given equation, (x+4)(x+2) represents a factored form of a quadratic expression. Understanding how to factor polynomials is essential for simplifying equations and solving for variable values.
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Quadratic Equations
A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. The equation in the question can be rearranged into this standard form after expanding the left side. Recognizing the structure of quadratic equations is crucial for applying various solving techniques, such as factoring, completing the square, or using the quadratic formula.
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Zero Product Property
The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must be zero. This principle is vital when solving equations like (x+4)(x+2) = 2x, as it allows us to set each factor equal to zero to find the possible solutions for x. Mastery of this property is fundamental in algebra for solving polynomial equations.
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