4.3-4.5 Review Solve Polynomials by Factoring

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Define factoring in the context of polynomials.

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Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

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What is the Factor Theorem?

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The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor.

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What is a polynomial?

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

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What does it mean for a polynomial to be in fully factored form?

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A polynomial is in fully factored form when it is expressed as a product of its linear factors and irreducible polynomials.

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What is the difference between real and complex roots?

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Real roots are solutions to a polynomial that are real numbers, while complex roots include imaginary numbers and are of the form a + bi.