2.4 Practice - Combining 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 combine polynomials?

Back

Combining polynomials involves adding or subtracting polynomial expressions by combining like terms.

Front

What are like terms in polynomials?

Back

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

Front

Simplify the expression: (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)

Back

-8n^2 - 8n + 3

Front

Simplify the expression: (4x^2 + x) - (x^2 + 2x)

Back

3x^2 - x

Front

What is the result of adding the polynomials: (2x + 5y) + (3x - 2y)?

Back

5x + 3y

Front

What is the expanded form of (x + 3)^3?

Back

(x + 3)(x + 3)(x + 3) or x^3 + 9x^2 + 27x + 27.

Front

What is the distributive property in relation to polynomials?

Back

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

Front

Multiply the polynomials: (5x + 2)(x^2 - 3x + 6)

Back

5x^3 - 13x^2 + 24x + 12

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 - x, the degree is 3.