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 4n^4 - 8n + 4, the degree is 4.

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

How do you subtract 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 (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

The result is -8n^2 - 8n + 3.

Front

What is the result of -7xy + x + y + x - 3xy?

Back

The result is -10xy + 2x + y.

Front

How do you simplify (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

Combine like terms to get 11x^4 + 2x^2 + 14x.

Front

What is the perimeter of a triangle with sides represented by polynomials?

Back

The perimeter is the sum of the lengths of all sides. For example, if the sides are represented by polynomials, add them together.

Front

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

Back

The result is 3x^3 + 5.