Classifying, Adding, Subtracting, & Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 3x^4 + 2x^2 - x, the degree is 4.

Front

Classify the polynomial: 2x^3 - 5x + 7

Back

Polynomial (specifically a trinomial, as it has three terms).

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 4x^2 - 6x - 13.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 - 3x) = 7x^2 - x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.

Front

What is the product of (a + b)(a - b)?

Back

The product is a^2 - b^2, known as the difference of squares.

Front

Find the area of a rectangle with length (x-5) and width (3x+1).

Back

3x^2 - 14x - 5.

Front

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

Back

25s^2 + 20s + 4.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, such as 3x^2.