How do you write a polynomial in standard form, then classify it by degree and number of terms #3k^5+4k^26k^55k^2#?
1 Answer
standard form:
number of terms:
degree of polynomial in standard form:
Explanation:
Determining the Standard Form of the Polynomial
Notice how your equation follows the general equation of a quintic function in standard form,
#3k^5+4k^26k^55k^2=0#
#color(green)(bar(ul(color(white)(a/a)3k^5k^2=0color(white)(a/a) )))#
Determining the Number of Terms
The number of terms of the polynomial in standard form can be found by first defining what a term is. A
For example (but not limited to):
 Single numbers:
#3, 56, 623, 6134, 23980#  Variables:
#x, r, u, a, f#  Number and variable:
#3x, 56r, 623u, 6134a, 23980f#
Going back to your equation, the terms would be the following, where the positive and negative signs are ignored after the first term:
#underbrace(3k^5)_color(red)("term")underbrace(k^2)_color(red)("term")=0color(white)(X),color(white)(X)# thus:
#color(green)(bar(ul(color(white)(a/a)"number of terms"=2color(white)(a/a))))#
Determining the Degree
To determine the degree, take the
#underbrace(3k^5)_color(red)("term")underbrace(k^2)_color(red)("term")=0#

#3k^color(darkorange)5color(teal)(>)color(darkorange)5# 
#k^color(darkorange)2color(teal)(>)color(darkorange)2#
As you can see, the highest exponent is
#color(green)(bar(ul(color(white)(a/a)"deg"(3k^5k^2)=5color(white)(a/a))))#