Adding and 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, 4x^3 + 3x^2 - 2x + 1 is a polynomial.

Front

What does it mean to add polynomials?

Back

Adding polynomials involves combining like terms from two or more polynomial expressions. Like terms are terms that have the same variable raised to the same power.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves taking the second polynomial and changing the sign of each term, then combining like terms with the first polynomial.

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 combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = 8x.

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 leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2, the leading coefficient is 5.

Front

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

Back

Combine like terms: 4x^4 + 7x^4 = 11x^4, 6x + 8x = 14x, -3x^2 + 5x^2 = 2x^2. The simplified expression is 11x^4 + 2x^2 + 14x.

Front

What is the result of (2x^2 + 5x - 7) + (3 - 4x^2 + 6x)?

Back

Combine like terms: 2x^2 - 4x^2 = -2x^2, 5x + 6x = 11x, -7 + 3 = -4. The result is -2x^2 + 11x - 4.

Front

How do you simplify (8p + 7 + 8p^2) - (p + 4p^4 - 6p^2) + (2p^2 + p + 1)?

Back

Distribute the negative sign and combine like terms: -4p^4 + 16p^2 + 8p + 8.