Answer:
[tex]1.\text{ }7x^4+5x^2+x-9[/tex]
[tex]2.\text{ }7x^6-4x^3+1/x[/tex]
Explanation:
Polynomials are expressions with terms composed of monomials.
A monomial is an expression formed by the product of a coefficient (constant numbers, like 3, 4/5, or even a root), and a literal part.
The literal part may consist of one or more letters and each letter may be raised to a non-negative integer number (positive or zero).
Hence, for instance, (2/9)x²y⁵z⁴³ is a monomial.
The given expressions are:
[tex]1.\text{ }7x^4+5x^2+x-9[/tex]
[tex]2.\text{ }7x^6-4x^3+1/x[/tex]
[tex]1.\text{ }7x^4+5x^2+x-9[/tex]
This expression is a polynomial formed by 4 terms or monomials.
The monomials are:
[tex]7x^4,\\ \\ 5x^2,\\ \\ x,\text{ }and\\ \\ 9[/tex]
The degrees of each monomial are:
[tex]7x^4,\text{ }degree\text{ }4\\ \\ 5x^2,\text{ }degree\text{ }2\\ \\ x,\text{ }degree\text{ }1,\text{ }and\\ \\ 9\text{ }degree\text{ }0[/tex]
Thus, the one with the greatest degree is [tex]7x^4[/tex] . It defines the degree of the of the polynomial; hence the polynomial has degree four and is classified as quartic polynomial of four terms.
[tex]2.\text{ }7x^6-4x^3+1/x[/tex]
This is not a polynomial, because the letter in the last term, i.e. 1/x has a negative power:
[tex]1/x=x^{-1}[/tex]
As stated above, the powers have to be positive integers or zero (for the constant term).
Some special names used to classify the polynomials are:
You can find other classifications in your book or in the internet.
