How many terms are in the polynomial $$3x^2 + 4x - 5$$ ?

There are 3 terms in the polynomial: $$3x^2$$ , $$4x$$ , and $$-5$$ .

A monomial is a polynomial with only one term. For example, $$5x^3$$ is a monomial.

A binomial is a polynomial with exactly two terms. For example, $$3x + 4$$ is a binomial.

A trinomial is a polynomial with exactly three terms. For example, $$x^2 + 2x + 1$$ is a trinomial.

How do you add polynomials?

To add polynomials, combine like terms. For example, $$(2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5$$ .

How do you subtract polynomials?

To subtract polynomials, distribute the negative sign and then combine like terms. For example, $$(5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2$$ .

What is the result of multiplying a polynomial by a monomial?

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, $$2x(3x^2 + 4x) = 6x^3 + 8x^2$$ .

What is the difference between a polynomial and a rational expression?

A polynomial is an expression with non-negative integer exponents, while a rational expression is a ratio of two polynomials. For example, $$\frac{2x^2 + 3}{x - 1}$$ is a rational expression.

What is the zero polynomial?

The zero polynomial is the polynomial that has all coefficients equal to zero. It is denoted as $$0$$ and has no degree.

What is the factor theorem?

The factor theorem states that if $$f(c) = 0$$ for a polynomial $$f(x)$$ , then $$x - c$$ is a factor of $$f(x)$$ .

Understanding Polynomials and Their Properties 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 standard form of a polynomial?

Back

3.

FLASHCARD QUESTION

Front

How do you classify a polynomial by degree?

Back

Polynomials can be classified by their degree: 0 (constant), 1 (linear), 2 (quadratic), 3 (cubic), and so on.

4.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

The leading coefficient is the coefficient of the term with the highest degree. In this case, it is 9.

7.

FLASHCARD QUESTION

Front

What is a monomial?

Back

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