Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Example: 2x^2 + 3x - 5.

Front

What is the degree of a polynomial?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms (terms with the same variable and exponent). Example: (2x^2 + 3x) + (4x^2 - 2x) = 6x^2 + x.

Front

How do you subtract polynomials?

Back

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

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property or the FOIL method. Example: (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is calculated as a^2 + 2ab + b^2. Example: (x + 3)^2 = x^2 + 6x + 9.

Front

What is a like term?

Back

Like terms are terms that have the same variable raised to the same power. Example: 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

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. Example: 5x is a monomial; 5x + 3 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. Example: 4x^3 + 2x^2 - x + 5.

Front

How do you simplify a polynomial?

Back

To simplify a polynomial, combine like terms and eliminate any unnecessary parentheses. Example: 3x + 2x - 5 = 5x - 5.