14.1 Add/Subtract 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 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 of its terms before combining like terms with the first polynomial.

Front

How do you identify like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, in the polynomial 4x^2 + 3x - 2x^2, the like terms are 4x^2 and -2x^2.

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 the polynomial 5x^3 + 2x^2 - x, the degree is 3.

Front

How do you combine like terms in the expression (3x^2 + 4x) + (2x^2 - 5x)?

Back

Combine like terms: (3x^2 + 2x^2) + (4x - 5x) = 5x^2 - 1x or 5x^2 - x.

Front

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

Back

Combine like terms: (1x^3 + 3x^3) + (2x^2 + 0) + (-1x - 4x) + 5 = 4x^3 + 2x^2 - 5x + 5.

Front

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

Back

Subtract the second polynomial: (5x^2 - 2x^2) + (3 - 1) = 3x^2 + 2.

Front

What is the result of (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

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

Front

What is the sum of (3x^3 + 3x^2 - 4x + 5) and (x^3 - 2x^2 + x - 4)?

Back

Combine like terms: (3x^3 + 1x^3) + (3x^2 - 2x^2) + (-4x + 1x) + (5 - 4) = 4x^3 + 1x^2 - 3x + 1.