What is a coefficient in a polynomial?

A coefficient is a numerical factor in a term of a polynomial. For example, in the term $$5x^2$$ , the coefficient is 5.

What is the leading coefficient?

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in $$4x^3 + 2x^2 - 5$$ , the leading coefficient is 4.

What is the purpose of polynomial long division?

Polynomial long division is used to divide polynomials to find the quotient and remainder, similar to numerical long division.

What is the relationship between synthetic division and the Remainder Theorem?

Synthetic division can be used to find the remainder of a polynomial when divided by a linear factor, which is directly related to the Remainder Theorem.

What does it mean for a polynomial to be divided by a linear factor?

Dividing a polynomial by a linear factor means finding how many times the linear factor can fit into the polynomial, resulting in a quotient and possibly a remainder.

What is the significance of the coefficients in synthetic division?

The coefficients are used in synthetic division to represent the polynomial being divided, and they are manipulated to find the quotient and remainder.

What is the final answer in polynomial division?

The final answer in polynomial division consists of the quotient and the remainder expressed as a fraction of the divisor.

How do you identify the coefficients of a polynomial?

The coefficients of a polynomial can be identified by looking at the numerical factors in front of each term. For example, in $$5x^7 + 3x^6 - 9x^4 + 4x^3 + 2x - 37$$ , the coefficients are $$5, 3, 0, -9, 4, 0, 2, -37$$ .

Polynomial and Synthetic Division Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

4.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

5.

FLASHCARD QUESTION

Front

What is the Factor Theorem?

Back

6.

FLASHCARD QUESTION

Front

How do you perform synthetic division?

Back

7.

FLASHCARD QUESTION

Front

What is the quotient in polynomial division?

Back

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