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. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power. For example, in 3x + 4x, you can combine to get 7x.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x + 3) + (4x + 5) = 6x + 8.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x + 3) - (2x + 1) = 3x + 2.

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 a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 5x^2, 5 is the coefficient.

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

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

Back

The result is 5x + 7.

Front

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

Back

The result is 2x^2 - x.

Front

How do you simplify (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

The simplified expression is 5b^4 - 2b^3 + 4.