Operations with 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, 2x^2 + 3x - 5 is a polynomial.

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 the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

How do you find the perimeter of a rectangle with polynomial dimensions?

Back

To find the perimeter of a rectangle, use the formula P = 2(length + width). If the length and width are polynomials, add them first, then multiply by 2.

Front

What is the formula for the area of a rectangle?

Back

The area of a rectangle is calculated using the formula A = length × width. If the dimensions are polynomials, multiply the two polynomial expressions.

Front

What does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression means combining like terms and reducing the expression to its simplest form.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

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

Back

The result of (x + 5)^2 is x^2 + 10x + 25.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to each term of the polynomial being subtracted, then combine like terms.

Front

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

Back

The result is -8n^2 - 8n + 3.