Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number exponents and coefficients, combined using addition, subtraction, and multiplication. Example: 4x^3 + 3x^2 - 2x + 1.

Front

What does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression means to combine like terms and reduce the expression to its simplest form. Example: 3x + 2x = 5x.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. Example: 4x^2 and 3x^2 are like terms.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. Example: (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 3x + 5.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. Example: In 5x^4 + 3x^2 - 2, the degree is 4.

Front

What is the perimeter of a rectangle in terms of its length (l) and width (w)?

Back

The perimeter P of a rectangle is given by the formula P = 2l + 2w.

Front

How do you multiply two binomials?

Back

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

Front

What is the square of a binomial?

Back

The square of a binomial (a + b)^2 is equal to a^2 + 2ab + b^2. Example: (x + 3)^2 = x^2 + 6x + 9.

Front

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

Back

The result of (x + 7)^2 is x^2 + 14x + 49.

Front

What is the product of (b + 3)(b^2 + 2b + 1)?

Back

The product is b^3 + 5b^2 + 7b + 3.