Simplifying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting 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 reduce the expression to 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, 3x² and 5x² are like terms.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part unchanged. For example, 3x + 5x = 8x.

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: -2x(3x² + 6x - 1) - (4x² + 5x + 9)

Back

-6x³ - 16x² - 3x - 9.

Front

Simplify: (3x² + 4x - 2) - (5x + 7)

Back

3x² - x - 9.

Front

Simplify: 5(3x + 2)

Back

15x + 10.

Front

Simplify: 5x²(2x - 3)

Back

10x³ - 15x².

Front

What is the result of subtracting polynomials?

Back

Subtracting polynomials involves distributing the negative sign and then combining like terms.