Polynomial Operations

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^2 + 3x - 5 is a polynomial.

Front

What are the degrees of polynomials?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 5.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 - 3) - (2x^2 + 4) = 3x^2 - 7.

Front

What is the product of two polynomials?

Back

The product of two polynomials is found by using the distributive property (FOIL for binomials). For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is a like term?

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 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, while 3x + 2 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 degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial. For example, 3x(2x^2 + x) = 6x^3 + 3x^2.

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 - 3)(x + 2) = 0, then x = 3 or x = -2.