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The Factoring method for solving Quadratic Equations

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					The Factoring method for solving Quadratic Equations
Here are three general types of polynomial equations in one variable ( a  0 ):
Linear: ax  b  0
Quadratic: ax2  bx  c  0
Cubic: ax3  bx2  cx  d  0

The ax2 term is called the quadratic term, the bx term is the linear term, and the c is the
constant term.

A root, or solution, of a polynomial equation is a value of the variable that satisfies the
equation.

For example, the roots of x 2  5x  24  0 are -3 and 8, because when you plug in either
of these values for x, the equation holds.

When a polynomial equation in x is written with 0 as one side, one way to solve the
equation is by factoring the other side into linear factors of the form ax+b.

This method of solving quadratic equations is called the factoring method, and relies on
the zero-product property.
The zero-product property states that ab  0 if an only if a  0 or b  0 .

To use the zero-product property to solve a polynomial equation,
1. write the equation with 0 as one side,
2. factor the other side of the equation, and
3. solve the equation obtained by setting each factor equal to 0.

Example:
Solve: x 2  x  30

x 2  x  30  0
( x  5)(x  6)  0

x5  0            x6  0
             or
x  5             x6


A number r is a zero of a function f if f(r) = 0. If one factor occurs twice as a factor of f,
this is called a double root.

For example, x( x  2) 2 has three roots, x, (x-2), and (x-2). Since (x-2) occurs twice, it is
called a double root.
Solving Quadratics by Factoring Practice problems:                               Score:    /5

Solve. Identify all double roots.

( x  1)(x  4)  0




z 2  3  4z




3r 2  4r  1




10t 2  9t  1




(u  3)(u  3)  8u




** ( x  1)3  ( x  1) 2  0




** A graphic artist is designing a poster that consists of a rectangular print with a uniform
border. The print is to be twice as tall as it is wide, and the border is to be 3 in. wide. If
the area of the poster is to be 680 in2 , find the dimensions of the print.

				
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posted:11/14/2011
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