How do you write a polynomial in standard form, then classify it by degree and number of terms #14x^2  8 + 5x  6x^2 + 2x#?
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 quadratic function in standard form,
#14x^28+5x6x^2+2x=0#
#14x^26x^2+5x+2x8=0#
#color(green)(bar(ul(color(white)(a/a)8x^2+7x8=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:
#underbrace(8x^2)_color(red)("term")+underbrace(7x)_color(red)("term")underbrace(8)_color(red)("term")=0color(white)(X),color(white)(X)# thus:
#color(green)(bar(ul(color(white)(a/a)"number of terms"=3color(white)(a/a))))#
Determining the Degree
To determine the degree, take the
#underbrace(8x^2)_color(red)("term")+underbrace(7x)_color(red)("term")underbrace(8)_color(red)("term")=0#

#8x^color(darkorange)2color(teal)(>)color(darkorange)2# 
#7x^color(darkorange)1color(teal)(>)color(darkorange)1# 
#8color(teal)(>)0#
As you can see, the highest exponent is
#color(green)(bar(ul(color(white)(a/a)"deg"(8x^2+7x8)=2color(white)(a/a))))#