 Carl Gauss provided a proof of the fundamental theorem of algebra at the age of 22.  Gauss is considered the prince of mathematics.  Gauss was able to add all the numbers from in a matter of seconds in grade school.  My greatest accomplishment is graduating from high school.

 What is a monomial? ◦ A monomial is a number or a product of numbers and variables with whole-number exponents, or a polynomial with one term. ◦ Ex - 5, 7x, -x^2, 6xy, -2.3x^3  What is a polynomial? ◦ A polynomial is a monomial or a sum or difference of a monomials. ◦ Ex. 6xy, x^2 + 2x, 3x +2y-4z,

 Domain-The set of all possible input values of a relation or function. (x values)  Range- The set of output values of a function or relation. (y values)  Origin- The intersection of the x- and y- axes in a coordinate plane. The coordinates of the origin are (0,0).  x-intercepts- x- coordinate(s) of the point(s) where a graph intersects the x-axis. y= x^2 -4

 What is degree of polynomial? ◦ The degree of a polynomial is the highest degree of the terms in the polynomial ◦ Ex. x^3+x^4-3x+2, the highest degree of any of the terms is 4. Thus the degree of the polynomial is 4.  What is a zero of a polynomial? ◦ A zero of a polynomial is the solution of a polynomial equation, f(x) = 0 ◦ Ex. 0 = x^2-4 = (x-2)(x+2), Then x-2=0 or x+2=0, therefore are zero’s of the polynomial are x=2 or x=-2. We can say f(2)=0 or f(-2)=0.

 Local Maximums and Local Minimum values- ◦ Local maximum is a function f, f(a) is a local maximum if there is an interval around a such that f(x) ‹ f(a) for every x- value in the interval except a. ◦ Local minimum is a function f, f(a) is a local minimum if there is an interval around a such that f(x) › f(a) for every x- value in the interval except a. f(x)=-(x^2)+4 (local maximum) f(x)= x^2 -4 (local minimum)

 What is a real number? ◦ A real number is a rational or irrational number. Every point on the number line represents a real number. ◦ Ex. 1, , 4/6,  What is a complex number? ◦ A complex number is any number that can be written as a +bi, where a and b are real numbers and i =. ◦ Ex. 4+6i, -7i, 4+0i= 4, 1/2i

 What is a real zero (real root)? ◦ A real zero is the solution of a polynomial equation, f(x) = 0 where x is a real number. ◦ Ex. f(x)=x^2-6x+9, has a real zero, f(3)=0  What is an complex zero (complex root)? ◦ A complex zero is the solution of a polynomial equation, f(x) = 0 where x is a complex number. ◦ In quadratic equation if we end up with f(x)= We know that x= and that the complex zeros are f( ) or f( )=0.

 (as x gets very large)  (as x gets very large with a negative value) f(x)= x^2 -4 f(x)= x^3 +4