Operations with 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 and coefficients. For example, 2x^2 + 3x + 1 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 4x^3 + 2x^2 + 5, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 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 the difference between a monomial and a polynomial?

Back

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

Front

What is the process of multiplying polynomials?

Back

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

Front

What is factoring in polynomials?

Back

Factoring is the process of breaking down a polynomial into simpler polynomials that, when multiplied together, give the original polynomial. For example, x^2 - 9 can be factored into (x - 3)(x + 3).

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 the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if (x - 2)(x + 3) = 0, then x - 2 = 0 or x + 3 = 0.

Front

How do you find the sum of two polynomials?

Back

To find the sum of two polynomials, combine like terms. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.