Adding and Subtracting Polynomial Expressions

Front

What is a polynomial expression?

Back

A polynomial expression is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents of variables. 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 simplify a polynomial by adding or subtracting terms that have the same variable raised to the same power.

Front

How do you add polynomial expressions?

Back

To add polynomial expressions, combine like terms by adding their coefficients while keeping the variable part unchanged.

Front

How do you subtract polynomial expressions?

Back

To subtract polynomial expressions, distribute the negative sign to the terms of the polynomial being subtracted, 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 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 (3x + 4y - 3z) - (2x - 6y + 7z)?

Back

The result is x + 10y - 10z.

Front

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

Back

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

Front

How do you simplify the expression (6x + 4x^4 - 3x^2) + (7x^4 + 5x^2 + 8x)?

Back

The simplified expression is 11x^4 + 2x^2 + 14x.