Ch 4.3 Polynomial Operations and Functions

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their exponents. For example, 2x^3 + 9x^2 + 5x + 27.

Front

How do you simplify the expression (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

Combine like terms: (4n^4 - 4n^4) + (-8n - 0) + (4 - 1) - 8n^2 = -8n^2 - 8n + 3.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, y^2 and 2y^2 are like terms.

Front

What is a leading coefficient in a polynomial?

Back

The leading coefficient is the number in front of the term with the highest exponent in a polynomial. For example, in 2x^3 + 5x^2, the leading coefficient is 2.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of the variable in the polynomial. For example, the degree of 2x^3 + 5x^2 is 3.

Front

What is the result of adding the polynomials (3x^2 + 2x) and (4x^2 + 5)?

Back

The result is (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

What is the difference between monomials, binomials, and polynomials?

Back

A monomial has one term, a binomial has two terms, and a polynomial has more than two terms.

Front

How do you identify the highest degree term in a polynomial?

Back

The highest degree term is identified by finding the term with the largest exponent. For example, in 5x^4 + 3x^2 + 2, the highest degree term is 5x^4.

Front

What is the process of polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial, similar to numerical long division.

Front

What is the result of subtracting the polynomial (2x^3 + 3x^2) from (5x^3 + 4x^2 + 1)?

Back

The result is (5x^3 - 2x^3) + (4x^2 - 3x^2) + 1 = 3x^3 + x^2 + 1.