Polynomials

Question 1

What is a polynomial in one variable x?

Accepted Answer

An expression made of terms like ax^n, where every power of x is a whole number (0, 1, 2, 3, \dots). Example: 3x^2 - 5x + 7. Note: \sqrt{x} and \frac{1}{x} are NOT allowed, because their powers are not whole numbers.

Question 2

What is the degree of a polynomial?

Accepted Answer

The highest power of the variable. In 4x^3 + 2x - 9 the highest power is 3, so the degree is 3. Just look for the biggest exponent.

Question 3

Name polynomials by degree: degree 1, 2 and 3.

Accepted Answer

Degree 1 = linear (e.g. 2x + 1). Degree 2 = quadratic (e.g. x^2 - 3x + 2). Degree 3 = cubic (e.g. x^3 + 1).

Question 4

What are monomial, binomial and trinomial?

Accepted Answer

Count the terms. 1 term = monomial (5x^2). 2 terms = binomial (x + 3). 3 terms = trinomial (x^2 + 2x + 1).

Question 5

What is the degree of a non-zero constant like 7?

Accepted Answer

The degree is 0. You can think of 7 as 7x^0, and the power is 0. (The number 0 itself is the zero polynomial and has no defined degree.)

Sample questions