Factoring Polynomials Completely

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What is factoring in mathematics?

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Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

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What is a polynomial?

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A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

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What does it mean to factor a polynomial completely?

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Factoring a polynomial completely means expressing it as a product of irreducible polynomials, meaning it cannot be factored further over the given number system.

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What is the first step in factoring a polynomial?

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The first step is to look for a common factor in all the terms of the polynomial and factor it out.

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What is the difference between factoring and expanding?

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Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get the original expression.

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What is a common factor?

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A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

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What is the significance of the zero product property in factoring?

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The zero product property states that if the product of two factors is zero, at least one of the factors must be zero, which is useful for solving polynomial equations.