Synthetic or long division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c) without using long division.

Front

What is the purpose of using a zero placeholder in synthetic division?

Back

A zero placeholder is used to maintain the correct degree of the polynomial when a term is missing, ensuring accurate calculations.

Front

How do you determine if (x - c) is a factor of a polynomial?

Back

To determine if (x - c) is a factor, perform synthetic division. If the remainder is zero, then (x - c) is a factor.

Front

What does the remainder represent in synthetic division?

Back

The remainder represents the value of the polynomial at the point x = c, and it indicates whether (x - c) is a factor.

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 (x - c).

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How do you handle missing terms in synthetic division?

Back

When handling missing terms, use a zero as a placeholder for the coefficient of the missing term.

Front

What is the result of dividing (2x^3 + 4x^2 - 5) by (x + 3) using synthetic division?

Back

The result is 2x^2 - 2x + 6 with a remainder of -23.

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

Back

The leading coefficient affects the degree of the resulting polynomial after division and influences the overall shape of the graph.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, from the highest degree to the lowest.

Front

How do you write the final answer after synthetic division?

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The final answer is written as the quotient polynomial plus the remainder over the divisor.