What is the end behavior of a polynomial?

The end behavior of a polynomial describes how the values of the polynomial behave as x approaches positive or negative infinity. For example, for a polynomial of even degree with a positive leading coefficient, both ends will rise.

What is a factor of a polynomial?

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder. For example, $$(x + 4)(x - 3)(x - 2)$$ are factors of the polynomial.

How do you find the zeros of a polynomial?

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. For example, for $$f(x) = (x + 4)(x - 3)(x - 2)$$ , the zeros are $$x = -4, 3, 2$$ .

What is the difference between a monomial and a polynomial?

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, $$3x^2$$ is a monomial, and $$2x^2 + 3x + 1$$ is a polynomial.

What is the standard form of a polynomial?

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, $$4x^3 - 2x^2 + 3x + 1$$ is in standard form.

What is a coefficient in a polynomial?

A coefficient is a numerical factor in a term of a polynomial. For example, in the term $$-19x^2$$ , -19 is the coefficient.

What is a constant term in a polynomial?

A constant term is a term in a polynomial that does not contain any variables. For example, in the polynomial $$2x^3 - 19x^2 + 38x + 24$$ , 24 is the constant term.

What is the Remainder Theorem?

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c). This helps in finding the value of the polynomial at specific points.

What is the Factor Theorem?

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0. This is used to find factors and zeros of polynomials.

Unit 3 Review Polynomials Flashcard

Student preview

16 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What are the real zeros of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

How do you add polynomials?

Back

4.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

5.

FLASHCARD QUESTION

Front

What is the leading coefficient of a polynomial?

Back

6.

FLASHCARD QUESTION

Front

What is polynomial long division?

Back

Polynomial long division is a method for dividing a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

7.

FLASHCARD QUESTION

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used when dividing by a linear factor. It is faster and requires less writing.

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