Adding & 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 4x^3 + 2x^2 - x + 7, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

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

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, 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

What is the result of subtracting (2a^2 + 5a + 3) from (a^2 - 3a - 4)?

Back

The result is a^2 + 8a + 7.

Front

What is the process of simplifying a polynomial expression?

Back

Simplifying a polynomial expression involves combining like terms and performing any necessary arithmetic operations to reduce the expression to its simplest form.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the polynomial function.

Front

How do you identify the leading term of a polynomial?

Back

The leading term of a polynomial is the term with the highest degree. For example, in the polynomial 5x^4 + 3x^2 - 2, the leading term is 5x^4.