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 them to get 7x.

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

How do you add two polynomials?

Back

To add two polynomials, combine like terms by adding the coefficients of terms with the same variable and exponent.

Front

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

Back

The result is 6x + 8 after combining like terms.

Front

What is the result of (5x^2 - 3x + 4) - (2x^2 + x - 1)?

Back

The result is 3x^2 - 4x + 5 after distributing the negative sign and combining like terms.

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, 2x^2 and 5x^2 are like terms.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, and 3x + 2 is 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. For example, 4x^3 + 2x^2 + x is in standard form.

Front

What is the result of (x^2 + 2x + 1) + (3x^2 - x + 4)?

Back

The result is 4x^2 + x + 5 after combining like terms.