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
. The numbers
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
f ( x) ax bx c
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
Solving Polynomial Equations
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
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
3 2i; 7i; 4i 3 (The two last ones are called pure imaginary
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
Square root property:
If x a and a is a non-negative real number, then x a .
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
Exponent Properties from Algebra 1 to remember:
a m a n a
a 0 1 (a 0)
To perform operations with radicals or rational
Operations with Polynomials
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:
a( x b) ax ab
Simplifying Radicals and Operations
Radical: an indicated root of a quantity (Ex.
Radicand: the expression under the radical symbol
Index or Root: in the radical
which represents the nth root of x, n is
the index; when no index appears
Multiplying and Dividing Rational Expressions
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
Applications of Radical Equations
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
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