Adding and Subtracting Polynomials

Front

What are like terms?

Back

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

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (4x - 2x^3) + (5x^3 - 4x + 5) simplifies to 3x^3 + 5.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 2x^3 + 9x^2 + 5x + 27.

Front

What is a polynomial?

Back

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

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 2x^3 + 5x^2 + 3, the degree is 3.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (x^5 + x^3) - (6x - x^3 + 6x^5) simplifies to -5x^5 + 2x^3 - 6x.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^2, 4 is the coefficient.

Front

What is a constant term in a polynomial?

Back

A constant term is a term in a polynomial that does not contain any variables. For example, in 2x^3 + 5, 5 is the constant term.

Front

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

Back

The result is 5x^2 + 2x - 2.

Front

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

Back

The result is 3x^3 + 5.