Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = 8x.

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 4x^3 + 2x^2 + 5, 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^2 + 5, the leading coefficient is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms from each polynomial. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x + 3) - (2x + 1) = 3x + 2.

Front

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

Back

The result is 9x + 7.

Front

What is the result of (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

The result is 11a^3 - 4a^2 - 14a - 7.

Front

What is the degree of the polynomial 3x^4 + 2x^2 + 5x?

Back

The degree is 4.