3.6 Long and Synthetic Division of Polynomials

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 than long division and involves using coefficients of the polynomial.

Front

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing the coefficients of the polynomial and the zero of the divisor (c) to the left.

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How do you find the zero of the divisor (x - c)?

Back

To find the zero of the divisor (x - c), set x - c = 0, which gives c as the value to use in synthetic division.

Front

What is the remainder in synthetic division?

Back

The remainder is the value left over after dividing the polynomial, which can be found at the bottom of the synthetic division setup.

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What does it mean if the remainder is zero?

Back

If the remainder is zero, it means that the polynomial is divisible by the divisor without any leftover, indicating that (x - c) is a factor of the polynomial.

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How do you handle missing terms in synthetic division?

Back

When there are missing terms in the polynomial, use a zero as a placeholder for the coefficient of that term.

Front

What is the result of dividing (2x³ - 5x - 7) by (x - 2) using synthetic division?

Back

The result is 2x² + 4x + 3 with a remainder of -1.

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What is the significance of the coefficients in synthetic division?

Back

The coefficients represent the terms of the polynomial, and they are used in the synthetic division process to calculate the quotient and remainder.

Front

What mistake did Cam make in his synthetic division?

Back

Cam did not use a zero placeholder for the x³ term, which is essential for accurate calculations.

Front

What is the purpose of using synthetic division?

Back

Synthetic division is used to simplify the process of dividing polynomials, making it quicker and easier to find the quotient and remainder.