5-1: monomials and polynomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables (e.g., 3x^2, -5, 7xy).

Front

What is a polynomial?

Back

A polynomial is an expression that consists of variables raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication (e.g., 4x^3 + 2x^2 - x + 7).

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable parts the same (e.g., (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 5).

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms (e.g., (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2).

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power (e.g., 3x^2 and 5x^2 are like terms, but 3x^2 and 4x are not).

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression (e.g., in 4x^3 + 2x^2 - x, the degree is 3).

Front

What is the product of a monomial and a polynomial?

Back

To multiply a monomial by a polynomial, distribute the monomial to each term in the polynomial (e.g., 3x(2x^2 + x - 4) = 6x^3 + 3x^2 - 12x).

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents (e.g., (x^a)^b = x^(a*b)).

Front

How do you simplify (2x^3y)^2?

Back

To simplify (2x^3y)^2, apply the power of a product property: (2^2)(x^(3*2))(y^2) = 4x^6y^2.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials, standing for First, Outside, Inside, Last (e.g., (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6).