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. ![]() Predicting the height of a person given the age of the person. Notice that there are only special classifications for polynomials according to the number of their terms if that number is three or less. Predicting the price of the car given the car model, year of manufacturing, mileage, engine capacity. Table 10.1 Classifying a Polynomial Based on the Number of Its Terms Number of Terms For example, you could rewrite the simple polynomial 2 x + 1 as 2 x + 1 x 0, but since x 0 = 1 (and anything multiplied by 1 equals itself), there's no reason to write x 0 at the end of the polynomial.īecause 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). Technically, the constant in a polynomial does have a variable attached to it, but the variable is raised to the 0 power. The equation is still not in its standard form, so let’s go ahead and isolate all terms on the left-hand side. (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. Find the values of x that satisfies the given equation: 4x 5 4x 4 + 73x 2 -18 (x -1)+ 73x 3. The constant in a polynomial has no variable written next to it.įor example, if you were to write the polynomial 2 x 3- 7 x 5 + 8 x + 1 in standard form, it would look like this: -7 x 5 + 2 x 3 + 8 x + 1. ![]() The largest exponent in the polynomial is called the degree, and the coefficient of the variable raised to that exponent is called the leading coefficient. A polynomial consists of the sum of distinct algebraic clumps (called terms), each of which consists of a number, one or more variables raised to an exponent, or both.
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