What is the Factor Theorem?

The Factor Theorem states that a polynomial $$f(x)$$ has a factor $$(x - c)$$ if and only if $$f(c) = 0$$ . For example, if $$f(x) = x^2 - 5x + 6$$ , then $$(x - 2)$$ is a factor because $$f(2) = 0$$ .

How do you expand a binomial expression?

To expand a binomial expression, use the Binomial Theorem or distribute. For example, $$(a + b)^2 = a^2 + 2ab + b^2$$ .

Like terms are terms that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms, while $$3x^2$$ and $$4x^3$$ are not.

What is the leading coefficient of a polynomial?

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

What is the standard form of a polynomial?

The standard form of a polynomial is written in descending order of the degree of its terms. For example, $$4x^3 + 2x^2 - x + 7$$ is in standard form.

How do you factor a polynomial?

To factor a polynomial, find the greatest common factor (GCF) or use methods like grouping, the difference of squares, or the quadratic formula. For example, $$x^2 - 9 = (x - 3)(x + 3)$$ .

What is synthetic division?

Synthetic division is a simplified form of polynomial long division used when dividing by a linear factor of the form $$(x - c)$$ . It is faster and involves fewer steps.

What is the significance of the zeroes of a polynomial?

The zeroes of a polynomial are the values of $$x$$ that make the polynomial equal to zero. They are important for graphing the polynomial and understanding its behavior.

Polynomial Operations 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 are the degrees of polynomials?

Back

3.

FLASHCARD QUESTION

Front

How do you add polynomials?

Back

4.

FLASHCARD QUESTION

Front

How do you subtract polynomials?

Back

5.

FLASHCARD QUESTION

Front

What is the product of two polynomials?

Back

6.

FLASHCARD QUESTION

Front

What is the quotient of two polynomials?

Back

7.

FLASHCARD QUESTION

Front

What is the Remainder Theorem?

Back

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