Adding & 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, 4x^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 + 3) + (4x + 5) = (2x + 4x) + (3 + 5) = 6x + 8.

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, (5x + 3) - (2x + 1) = (5x - 2x) + (3 - 1) = 3x + 2.

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 - x, the degree is 3.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 3x^4 + 2x^3 - x, the leading coefficient is 3.

Front

What is the sum of (4a + 6ab - b) + (-2a - ab + 3b)?

Back

The sum is 2a + 5ab + 2b.

Front

What is the result of simplifying (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

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

Front

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

Back

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

Front

Which of the following are like terms: 2 and 2x, y^3 and x^3, y and x, -3x and 3x?

Back

-3x and 3x are like terms.