Synthetic Division Basics

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Synthetic Division

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A simplified method for dividing polynomials, especially useful for dividing by linear factors.

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Step 1: Write Coefficients

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List coefficients of the dividend polynomial.

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Step 2: Identify Divisor

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Use the zero of the linear divisor x - c.

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Step 3: Bring Down First Coefficient

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Write the first coefficient of the dividend below the line.

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Step 4: Multiply and Add

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Multiply the divisor's zero by the number below the line, add to next coefficient.

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Step 5: Repeat Process

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Continue multiplying and adding for all coefficients.

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Step 6: Last Number

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The last number is the remainder.

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Result Interpretation

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The numbers below the line form the coefficients of the quotient.

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Example: Divide 2x^3 + 3x^2 - 5x + 6 by x - 2

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Quotient: 2x^2 + 7x + 9, Remainder: 24

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Common Mistake: Wrong Coefficients

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Ensure all coefficients, including zeros, are listed.