Adding and Subtracting Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 5 is a polynomial.

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.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

How do you subtract polynomials?

Back

To subtract polynomials, you distribute the negative sign to the terms of the polynomial being subtracted and then combine like terms.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

Front

What is the coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 3x^2, 3 is the coefficient.

Front

Simplify: (x + 2x^2) + (4x^2 + 7x)

Back

6x^2 + 8x.

Front

Simplify: (2x + 5y - z) + (-6x - 4y + 7z)

Back

-4x + y + 6z.

Front

Simplify: (5x + x^2 - 4) - (4x - x^2 + 6)

Back

2x^2 + x - 10.

Front

Find the sum: (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8)

Back

3y^3 + 7y^2 - 4y + 3.