Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 5 is a polynomial.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x and -5x are like terms, while 3x and 3x^2 are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2x^2 + 4x^2) + (3x + 5x) = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x + 4) - (2x + 1) = 3x + 4 - 2x - 1 = (3x - 2x) + (4 - 1) = x + 3.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. For example, 2x^3 + 3x^2 + x + 5 is in standard form.

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 the polynomial 4x^3 + 2x^2 + 5, the degree is 3.

Front

What is the coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in the term 5x^2, 5 is the coefficient.

Front

What is the result of (3x + 4y - 3z) - (2x - 6y + 7z)?

Back

The result is x + 10y - 10z.

Front

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

Back

The result is 2x^3 - 6x^2 + 9x.

Front

What is the result of adding (3x^2 + 2x + 1) + (2x^2 - 4x - 5) + (3x - 1)?

Back

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