Operations with Polynomials

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 does it mean to simplify a polynomial?

Back

Simplifying a polynomial involves combining like terms and reducing the expression to its simplest form.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

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) = 6x^2 + 3x + 5.

Front

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

Back

The result of (a + b)^2 is a^2 + 2ab + b^2, according to the binomial expansion.

Front

What is the product of two binomials (x + a)(x + b)?

Back

The product of two binomials (x + a)(x + b) is x^2 + (a + b)x + ab.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a - b)(a + b).

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, 3x(2x^2 + 4x) = 6x^3 + 12x^2.

Front

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

Back

The result of (2x + 5)^2 is 4x^2 + 20x + 25.

Front

How do you factor the expression x^2 - 9?

Back

The expression x^2 - 9 can be factored as (x - 3)(x + 3) using the difference of squares.