Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents of variables. 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 - 7, the degree is 4.

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) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 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) = 5x^2 - 3 - 2x^2 - 4 = 3x^2 - 7.

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

Front

What is the result of (a + b)^2?

Back

The result of (a + b)^2 is a^2 + 2ab + b^2, which is known as the square of a binomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a parenthesis.

Front

How do you simplify (2x + 3) + (4x - 5)?

Back

To simplify, combine like terms: (2x + 4x) + (3 - 5) = 6x - 2.

Front

What is the result of (x^2 - 3x - 2) + (5x^2 + 10x - 5)?

Back

The result is 6x^2 + 7x - 7.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^3, 4 is the coefficient.