Polynomial Functions
EQ:
A polynomial function of degree n is a function in the form
P ( x) an x n an 1 x n 1 L a1 x a0
an 0
. The numbers
The number
a0
where n is a nonnegative integer and
a0 , a1 , a2 ,K , an
are coefficients of the polynomial.
is the c

The Quadratic Formula and the Discriminant
EQ:
In
f ( x) ax bx c
2
the quadratic formula will yield the real or non-
real solutions. For non-real (complex/imaginary) solutions, the
parabola will not cross the x-axis and for the real solutions it crosses
t

Solving Polynomial Equations
EQ:
Some polynomial equations can be solved by factoring. Zeros of
the function sometimes can be found by factoring.
Rational Root Theorem: If a polynomial has integer coefficients,
then every rational root has the following f

Complex Numbers
EQ:
A complex number is any number that can be written as a + bi, where "a" is
the real part and "bi" is the imaginary part. Real numbers are complex
numbers where
b 0.
Examples:
3 2i; 7i; 4i 3 (The two last ones are called pure imaginary

Radical Inequalities
EQ:
A radical inequality is an inequality that contains a variable within a
radical. You can solve by graphing or using algebra.
Solving Square Root Inequalities Graphically:
1) Using the graphing calculator, enter the left side of t

Completing the Square
EQ:
Square root property:
If x a and a is a non-negative real number, then x a .
2
In other words,
to solve a quadratic equation, you can take the square root of both
sides of the equation. Be sure to consider the positive and negati

Operations with Radicals and Rational Expressions
EQ:
Exponent Properties from Algebra 1 to remember:
a m a n a
a 0 1 (a 0)
1
a
a
1
a
b
1
b
a
mn
am
mn
a
n
a
a b
m
a
m n
n
a b
m
m
a
b
a mn
an
n
b
To perform operations with radicals or rational

Operations with Polynomials
EQ:
To add polynomials, add like terms. To subtract polynomials, add the opposite of the
second polynomial. Write polynomial in standard form.
To multiply a polynomial use the distributive property:
then
a( x b) ax ab
combine l

Simplifying Radicals and Operations
EQ:
Radical: an indicated root of a quantity (Ex.
;
)
3
24
35
Radicand: the expression under the radical symbol
Index or Root: in the radical
which represents the nth root of x, n is
n
x
the index; when no index appears

Multiplying and Dividing Rational Expressions
EQ:
A rational expression is a quotient of two polynomials.
(Ex. of rational expressions:
).
x 2 4 10 x 3
; ;
x2 x x7
Simplifying, multiplying or dividing rational expressions works the same way as
multiplying

Applications of Radical Equations
EQ:
Radical equations are used to represent relationships between various objects.
Substitute known values into the formula given and then use inverse
operations to isolate the variable remaining. Usually a calculator wil

Solving Radical Equations II
EQ:
Things to remember about solving radical equations:
1) A radical equation contains a variable in the radicand.
2) Two types of radical equations: those with just one radical expression
where you isolate the radical express