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.

Tags

CCSS.HSA.APR.A.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, (2x^2 + 3) - (x^2 + 1) = (2x^2 - x^2) + (3 - 1) = x^2 + 2.

Tags

CCSS.HSA.APR.A.1

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.

Tags

CCSS.6.EE.A.2B

Front

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

Back

The result is x^2 + x + 1.

Tags

CCSS.HSA.APR.A.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.

Tags

CCSS.HSA.APR.A.1

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.

Tags

CCSS.7.EE.A.1

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.