Adding and 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 does it mean to add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Tags

CCSS.HSA.APR.A.1

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms.

Tags

CCSS.HSA.APR.A.1

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power, allowing them to be combined.

Tags

CCSS.6.EE.A.2B

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part unchanged.

Tags

CCSS.7.EE.A.1

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

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.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees.

Front

How do you add the polynomials (-7x^3 - 2x^4) and (4x^3 + 4x^4)?

Back

Combine like terms: (-2x^4 + 4x^4) + (-7x^3 + 4x^3) = 2x^4 - 3x^3.

Tags

CCSS.HSA.APR.A.1

Front

How do you subtract the polynomial (x^4 + x + 4) from (-2x^3 - 8x - 3)?

Back

Change the signs of the second polynomial and combine: (x^4 + x + 4) - (-2x^3 - 8x - 3) = x^4 + 2x^3 + 9x + 7.

Tags

CCSS.HSA.APR.A.1