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 and coefficients. For example, 4x^2 - 21x + 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 polynomial. For example, in the polynomial 7x^3 - 8x^2 + 9, the degree is 3.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^2 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, 4x^2 - 21x + 5 is a trinomial.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8) = 3y^3 + 7y^2 - 4y + 3.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x^3 + 3x^2 + 5) - (x^3 - 2x^2 + x - 4) = 2x^3 + 5x^2 - x + 9.

Front

What is the product of two binomials?

Back

The product of two binomials can be found using the distributive property (FOIL method). For example, (3x - 6)(7x + 7) = 21x^2 - 21x - 42.

Front

What are like terms?

Back

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

Front

What is the coefficient in a polynomial?

Back

The coefficient is the numerical factor in front of a term in a polynomial. For example, in 4x^2, 4 is the coefficient.