The Degree of The Zero Polynomial
Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial. It has no nonzero terms, and so, strictly speaking, it has no degree either. The above rules for the degree of sums and products of polynomials do not apply if any of the polynomials involved is the zero polynomial.
It is convenient, however, to define the degree of the zero polynomial to be minus infinity, −∞, and introduce the rules
and
For example:
- The degree of the sum is 3. Note that .
- The degree of the difference is . Note that .
- The degree of the product is .
The price to be paid for saving the rules for computing the degree of sums and products of polynomials is that the general rule
breaks down when .
Read more about this topic: Degree Of A Polynomial
Famous quotes containing the word degree:
“Take but degree away, untune that string,
And hark what discord follows!
...
Force should be right, or, rather, right and wrong—
Between whose endless jar justice resides—
Should lose their names, and so should justice too.
Then everything includes itself in power,
Power into will, will into appetite;
And appetite, an universal wolf,
So doubly seconded with will and power,
Must make perforce an universal prey,
And last eat up himself.”
—William Shakespeare (1564–1616)