Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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Solving Polynomial Equations

A polynomial equation is an equation that can be written in the form: 

an xn + an - 1 xn - 1+ an - 2 xn - 2 + ... + a1 x + a0 = 0.

We will learn to solve this type of equation both algebraically and graphically.


Solving Polynomial Equations by Factoring

With this method, we use the zero product property, just as we did to solve quadratic equations. In general, if a number is a solution to a polynomial equation f(x) = 0, then the following are true: 

• (x - a) is a factor of f(x)

• a is a zero of the function f(x)

• a is an x-intercept of the graph of f(x)


Solving Polynomial Equations by the Root Method

Recall that to solve x2 = C, C 0, we take the square root of both sides and use the symbol ± to indicate both the positive square root and the negative square root as solutions. So the solutions are x = ±.

We can solve the equation x3 = C, where C is any real number, by taking the cube root of both sides. The solution to this equation would then be . There is only one real cube root of a number, so there is oe È$ only one solution to this equation.

In general, when n is even, there will be two real nth roots and when n is odd, there will be only one nth root. So the Root Method is:

The real solutions of the equation xn = C are found by taking the nth root of both sides:

if n is odd, and if n is even


Many real world models involve polynomial equations which either are not factorable or are extremely difficult to factor. In these cases, we need to rely on Graphical Methods.