Add and Subtract Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 4x^2 + 3x - 5 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. For example, (2x + 3) + (4x - 5) = 6x - 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

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, 2x + 3x = 5x.

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. For example, in 4x^3 + 2x^2 - x, the degree is 3.

Front

What is the result of adding (4x - 2x^3) + (5x^3 - 4x + 5)?

Back

The result is 3x^3 + 5.

Tags

CCSS.HSA.APR.A.1

Front

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

Back

The result is 7x + 5y.

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

Tags

CCSS.HSA.APR.A.1

Front

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

Back

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

Tags

CCSS.HSA.APR.A.1

Front

What is the result of combining like terms in 8x^3y + 3x^2y + 4xy + 5x^2y + 2xy + 7x^2y?

Back

The result is 8x^3y + 15x^2y + 6xy.

Tags

CCSS.7.EE.A.1