Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number exponents and coefficients. For example, 3x^2 + 2x + 1 is a polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

Front

How do you add polynomials?

Back

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

Front

What are like terms?

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, while 3x^2 and 4x are not.

Front

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

Back

The result is x^2 + x + 1.

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^2 + 2x) - (x^2 + x) = 3x^2 + 2x - x^2 - x = 2x^2 + x.

Front

What is the perimeter of a rectangle with length x and width y?

Back

The perimeter P of a rectangle is given by the formula P = 2(length + width). If length = x and width = y, then P = 2(x + y) = 2x + 2y.

Front

What is the result of (5x - y) + (2x + 6y)?

Back

The result is 7x + 5y.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 2x + 1 is a trinomial.