Polynomial Operations

Front

What are like terms?

Back

Like terms are terms that have the same variables raised to the same powers. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variables and exponents. For example, in 5x + 2 + 4x - 5, combine 5x and 4x to get 9x, and combine 2 and -5 to get -3, resulting in 9x - 3.

Front

What is the result of (x - 2)(3x^2 - 2x + 1)?

Back

The result is 3x^3 - 8x^2 + 5x - 2.

Front

What is the perimeter of a parallelogram with sides of length x and y?

Back

The perimeter P of a parallelogram is given by the formula P = 2(x + y).

Front

What is the result of (x^3 - x^2 + 4) - (3x^3 - 2x^2 + 3)?

Back

The result is -2x^3 + x^2 + 1.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^3 - 4x^2 + 3x - 5 is a polynomial.

Front

What is the degree of a polynomial?

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 + 7, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, and 3x + 2 is a polynomial.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.