Chapter 10.3 – Introduction to Polynomials

Flashcards covering key vocabulary, classifications, degree rules, evaluation procedures, and simplification techniques for polynomials as presented in Section 10.3 of the lecture.

What is a "term" in polynomial vocabulary?

A number or a product of a number and variables raised to powers.

Define the "coefficient" of a term.

The numerical factor of a term.

What is a "constant" term in a polynomial?

A term that is only a number (contains no variables).

Give the formal definition of a "polynomial."

A sum of terms involving variables raised to whole-number exponents, with no variables in any denominator.

How many terms are in the polynomial 7x^5 + x^2y^2 − 4xy + 7?

Four terms: 7x^5, x^2y^2, –4xy, and 7.

What are the coefficients of the terms in 7x^5 + x^2y^2 − 4xy + 7?

7 (for 7x^5), 1 (for x^2y^2), –4 (for –4xy), and 7 (for the constant 7).

Differentiate between a monomial, binomial, and trinomial.

Monomial: one term; Binomial: two terms; Trinomial: three terms.

How do you find the degree of a term?

Add the exponents of all variables in the term; a constant has degree 0.

What is the degree of 5a^4b^3c?

8 (4 + 3 + 1).

What is the degree of the polynomial 9x^3 – 4x^2 + 7?

3 (the highest degree among its terms).

When evaluating a polynomial, what operation is performed?

Replace each variable with the given value and simplify.

Evaluate 2x^3 – 3x + 4 when x = –2.

–6.

What does it mean to "combine like terms" in a polynomial?

Add or subtract terms that have exactly the same variables raised to exactly the same powers using the distributive property.

Rewrite 2x + x^4 in descending powers with no missing powers.

x^4 + 0x^3 + 0x^2 + 2x + 0.