Identify, Add, and Subtract Polynomials

Front

What is a polynomial?

Back

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

Front

What is the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the leading coefficient is 4.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2+4)x^2 + (3+5)x = 6x^2 + 8x.

Front

What is a constant term in a polynomial?

Back

A constant term is a term in a polynomial that does not contain any variables. For example, in the polynomial 3x^2 + 2x + 5, the constant term is 5.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^3 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 2x + 1 is a trinomial.

Front

How do you subtract polynomials?

Back

To subtract polynomials, change the sign of the polynomial being subtracted and then add the resulting polynomials. For example, (3x^2 + 2x) - (x^2 + 4x) = (3x^2 - x^2) + (2x - 4x) = 2x^2 - 2x.

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 5x^4 + 3x^2 - 2, the degree is 4.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.