Question

Classify by the DEGREE: 4x³ - 5x² + 2x - 1

Answer 1

Answer:

For example, if you were to write the polynomial 2x3- 7x5 + 8x + 1 in standard form, it would look like this: -7x5 + 2x3 + 8x + 1. (Note that each term's variable has a lower power than the term to its immediate left.) The degree of this polynomial is 5, its leading coefficient is -7, and the constant is 1.

Step-by-step explanation:

Technically, the constant in a polynomial does have a variable attached to it, but the variable is raised to the 0 power. For example, you could rewrite the simple polynomial 2x + 1 as 2x + 1x0, but since x0 = 1 (and anything multiplied by 1 equals itself), there's no reason to write x0 at the end of the polynomial.

Because there are so many different kinds of polynomials (52 flavors at last check, including pistachio), there are two techniques that are used to classify them, one based on the number of terms a polynomial contains (see Table 10.1), and one based on the degree of the polynomial (see Table 10.2).

Table 10.1 Classifying a Polynomial Based on the Number of Its Terms

Number of Terms Classification Example

1 monomial 19x2

2 binomial 3x3 - 7x2

3 trinomial 2x2 + 5x - 1

Notice that there are only special classifications for polynomials according to the number of their terms if that number is three or less. Polynomials with four or more terms are either classified according to degree or just described with the ultra-generic (and not very helpful) label "polynomial." (It's just as specific as labeling you a "human being.")

Table 10.2 Classifying a Polynomial Based on Its Degree

Degree Classification Example

0 constant 2x0 or 2

1 linear 6x1 + 9 or 6x + 9

2 quadratic 4x2 - 25x + 6

3 cubic x3 - 1

4 quartic 2x4 - 3x2 + x - 8

5 quintic 3x5 - 7x3 - 2