f 2 ' 2
2
& 6 2 % 1,
f(a + b) = (a + b)
2
- 6(a + b) + 1,
and
f(x + 1) = (x + 1)
2
- 6(x + 1) + 1.
where the ai
are complex numbers and (Of course, the coefficients a0
, ..., an a may be
0
Ö 0.
real numbers, since a real number is a special case of a complex number.)
Thus a first degree polynomial is of the form ax + b and a second degree polynomial of the
form ax
2
+ bx + c, with a Ö 0 in both cases. A non-zero constant a is a polynomial of degree
zero; the constant zero is also a polynomial, but it is not assigned a degree.
The polynomial equation y = x
2
- 6x + 1 defines y to be a function of x on the domain of
all complex numbers; that is, it provides a rule for assigning a unique complex number y to each
complex number x. The table
x 4 3 2 1 0 i 2i
y = x
2
- 6x + 1 -7 -8 -7 -4 1 -6i -3 - 12i
