Adding and Subtracting 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 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 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

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^2 and 5x^2 are like terms.

Front

What is the process of subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the terms of the polynomial being subtracted, then combine like terms.

Front

What is the result of adding (2x^2 + 5x - 7) and (3 - 4x^2 + 6x)?

Back

The result is -2x^2 + 11x - 4.

Front

How do you simplify the expression (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

First, distribute the negative sign: 6b^3 + 6 - b^4 - 8b^3 + 6b^4 - 2. Then combine like terms to get 5b^4 - 2b^3 + 4.

Front

What is the importance of combining like terms in polynomial operations?

Back

Combining like terms simplifies the expression, making it easier to work with and understand.

Front

What is the sum of (3y^2 + y^3 - 5) and (4y^2 - 4y + 2y^3 + 8)?

Back

The sum is 3y^3 + 7y^2 - 4y + 3.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.