Simplifying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean to simplify a polynomial?

Back

To simplify a polynomial means to combine like terms and express the polynomial in its simplest form.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

Simplify: (3 - 2x + 2x^2) + (4x - 5 + 3x^2)

Back

5x^2 + 2x - 2.

Front

What is the result of multiplying two binomials?

Back

The result of multiplying two binomials can be found using the distributive property or the FOIL method (First, Outside, Inside, Last).

Front

Simplify: 2x(-2x - 3)

Back

-4x^2 - 6x.

Front

What is the area of a rectangle with length (2x + 3) and width (4x + 2)?

Back

Area = (2x + 3)(4x + 2) = 8x^2 + 14x + 6.

Front

What is the product of (5x + 1)(x + 4)?

Back

5x^2 + 21x + 4.