How do you factor a polynomial?

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

What is the greatest common factor (GCF)?

The GCF of two or more terms is the largest expression that divides each of the terms without leaving a remainder. For example, the GCF of $$6x^2$$ and $$9x$$ is $$3x$$ .

What is the difference of squares?

The difference of squares is a special factoring case where $$a^2 - b^2 = (a - b)(a + b)$$ .

What is a rational expression?

A rational expression is a fraction where the numerator and the denominator are both polynomials. For example, $$\frac{2x + 3}{x^2 - 1}$$ is a rational expression.

How do you divide polynomials?

To divide polynomials, use long division or synthetic division. For example, dividing $$x^3 + 2x^2 + x$$ by $$x + 1$$ .

What is the remainder theorem?

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

What is synthetic division?

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form $$x - c$$ .

What is the significance of the leading coefficient?

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the polynomial function.

Polynomial Operations Review 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 does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression involves combining like terms and reducing the expression to its simplest form.

4.

FLASHCARD QUESTION

Front

How do you add polynomials?

Back

5.

FLASHCARD QUESTION

Front

How do you subtract polynomials?

Back

6.

FLASHCARD QUESTION

Front

What is the product of two binomials?

Back

7.

FLASHCARD QUESTION

Front

What is the formula for the square of a binomial?

Back

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