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, 4x^3 + 3x^2 - 2x + 1 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 the polynomial 5x^4 + 3x^2 - 2, the degree 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 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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, while 3x^2 and 4x are not.

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 + 1) = (5x^2 - 2x^2) + (3 - 1) = 3x^2 + 2.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 4x^3 + 2x^2 - x + 5 is in standard form.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, such as 3x^2. A polynomial can have multiple terms, such as 2x^2 + 3x + 1.

Front

What is the coefficient in a polynomial?

Back

The coefficient is the numerical factor in front of a variable in a term. For example, in 7x^3, 7 is the coefficient.

Front

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property (FOIL for binomials) to multiply each term in one polynomial by each term in the other. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the result of (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The result is 11x^4 + 2x^2 + 14x.