How many solutions does this system of equations have?
1 answer:
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Answer:
- The term with the greatest degree is
- The polynomial has degree 4 and is classified as a quadratic polynomial of 4 terms.
- It is not a polynomial.
Explanation:
<em>Polynomials</em> are expressions with terms composed of <em>monomials</em>.
A <em>monomial</em> 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:
This expression is a polynomial formed by <em>4 terms </em>or monomials.
The monomials are:
The degrees of each monomial are:
Thus, the one with the <em>greatest degree</em> is . It defines the degree of the of the polynomial; hence <em>the polynomial has degree four and is classified as quartic polynomial of four terms.</em>
This is <em>not a polynomial</em>, because the letter in the last term, i.e. 1/x has a negative power:
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:
- Degree 1 – linear
- Degree 2 – quadratic
- Degree 3 – cubic
- Degree 4 – quartic
- Degree 5 – quintic
You can find other classifications in your book or in the internet.