retake ASSIGN Classify/Add/Subtract/Multiply/DividePolynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

Front

How do you classify a polynomial by its degree?

Back

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

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term (e.g., 3x), a binomial has two terms (e.g., x + 4), and a trinomial has three terms (e.g., x^2 + 2x + 1).

Front

What is the process of adding polynomials?

Back

To add polynomials, combine like terms. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^2 + 2) - (x^2 + 4) = 3x^2 - x^2 + 2 - 4 = 2x^2 - 2.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (also known as the FOIL method for binomials). For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the result of multiplying x^2 by (2x + 3)?

Back

The result is 2x^3 + 3x^2.

Front

What is the result of the expression (x + 4)(x - 4)?

Back

The result is x^2 - 16.

Front

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

Back

The simplified expression is -8n^2 - 8n + 3.

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.