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, 3x^2 + 2x - 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 does it mean to subtract polynomials?

Back

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then 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, 3x^2 and 5x^2 are like terms.

Front

How do you simplify the expression (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

Combine like terms: (4n^4 - 4n^4) - 8n^2 - 8n + (4 - 1) = -8n^2 - 8n + 3.

Front

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

Back

Combine like terms: (x^2 + x^2) + (5x - 4x) + (-4 - 6) = 2x^2 + x - 10.

Front

How do you add the polynomials (2x + 5y - z) + (-6x - 4y + 7z)?

Back

Combine like terms: (2x - 6x) + (5y - 4y) + (-z + 7z) = -4x + y + 6z.

Front

What is the simplified form of (4a^3 - 8a - 4a^2) + (7a^3 - 7 - 6a)?

Back

Combine like terms: (4a^3 + 7a^3) + (-4a^2) + (-8a - 6a) - 7 = 11a^3 - 4a^2 - 14a - 7.

Front

What is the result of (x + 2x^2) + (4x^2 + 7x)?

Back

Combine like terms: (2x^2 + 4x^2) + (x + 7x) = 6x^2 + 8x.

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 3x^3 + 2x^2 - x, the degree is 3.