Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor 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).

Front

How do you handle coefficients of zero in synthetic division?

Back

If a coefficient is zero, you still include it in the setup. It represents a missing term in the polynomial.

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?

Back

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?

Back

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?

Back

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?

Back

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

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Perform synthetic division on (3x^3 - 2x^2 - 7x + 6) ÷ (x + 1). What is the quotient?

Back

The quotient is 3x^2 - 5x - 2.

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Perform synthetic division on (2x^3 + 7x^2 - 6x - 8) ÷ (x + 4). What is the quotient?

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