What are like terms in polynomials?

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, $$2x^2$$ and $$5x^2$$ are like terms, while $$2x^2$$ and $$3x$$ are not.

What is the degree of a polynomial?

The degree of a polynomial is the highest power of the variable in the polynomial. For example, the degree of $$4x^3 + 2x^2 - x + 7$$ is 3.

What is the leading coefficient of a polynomial?

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

How do you factor a polynomial?

Factoring a polynomial involves expressing it as a product of its factors. For example, $$x^2 - 9$$ can be factored as $$(x - 3)(x + 3)$$ .

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, $$3x$$ is a monomial, and $$2x^2 + 3x - 5$$ is a polynomial.

What is the zero product property?

The zero product property states that if the product of two or more factors is zero, then at least one of the factors must be zero. For example, if $$(x - 2)(x + 3) = 0$$ , then either $$x - 2 = 0$$ or $$x + 3 = 0$$ .

What is synthetic division?

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form $$(x - c)$$ . It is faster than polynomial long division and is used primarily for polynomials of one variable.

What is the remainder theorem?

The remainder theorem states that when a polynomial $$f(x)$$ is divided by $$(x - c)$$ , the remainder is equal to $$f(c)$$ .

Operations with Polynomials CFA Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

2.

FLASHCARD QUESTION

Front

What does it mean to add polynomials?

Back

Tags

CCSS.HSA.APR.A.1

3.

FLASHCARD QUESTION

Front

What is the process of subtracting polynomials?

Back

Tags

CCSS.HSA.APR.A.1

4.

FLASHCARD QUESTION

Front

How do you multiply a polynomial by a monomial?

Back

Tags

CCSS.HSA.APR.A.1

5.

FLASHCARD QUESTION

Front

What is the result of multiplying two polynomials?

Back

The result of multiplying two polynomials is a new polynomial formed by multiplying each term of the first polynomial by each term of the second polynomial and then combining like terms.

Tags

CCSS.HSA.APR.A.1

6.

FLASHCARD QUESTION

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of lower degree, similar to long division with numbers. It involves dividing the leading term of the dividend by the leading term of the divisor, multiplying, and subtracting.

Tags

CCSS.HSA.APR.D.6

7.

FLASHCARD QUESTION

Front

What is a quotient in polynomial division?

Back

Tags

CCSS.HSA.APR.D.6

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