Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c). It is faster and requires less writing than long division.

Front

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing down the coefficients of the polynomial and the value of c from the divisor (x - c).

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How do you handle coefficients of zero in synthetic division?

Back

If a polynomial has missing degrees (coefficients of zero), you still include a zero in the synthetic division setup to maintain the correct place value.

Front

What is the result of synthetic division?

Back

The result of synthetic division is a polynomial quotient and a remainder, which can be expressed as: Quotient + Remainder/(x - c).

Front

How do you find the quotient in synthetic division?

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To find the quotient, bring down the leading coefficient and multiply it by c, then add it to the next coefficient, repeating this process until all coefficients are processed.

Front

What does the remainder represent in synthetic division?

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The remainder represents the value of the original polynomial evaluated at x = c, indicating how much is left over after division.

Front

Perform synthetic division on (2x^3 - 5x - 7) ÷ (x - 2). What is the quotient?

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The quotient is 2x^2 + 4x + 3.

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Perform synthetic division on (2x^3 + 5x^2 + 9) ÷ (x + 3). What is the quotient?

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The quotient is 2x^2 - x + 3.

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Perform synthetic division on (3x^3 + 5x - 1) ÷ (x + 1). What is the quotient?

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The quotient is 3x^2 - 3x + 8.

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What is the significance of the leading coefficient in synthetic division?

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The leading coefficient determines the degree of the resulting polynomial and influences the shape of the graph of the polynomial.