5.2 Solving Quadratic Equations by Factoring

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5.2 Solving Quadratic Equations by Factoring
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Objectives

1. Factor quadratic expressions and solve quadratic
   equations by factoring.
2. Find zeros of quadratic functions.
3. Assignment 23-87 odd

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Recall multiplying these binomials to get the
standard form for the equation of a quadratic
function
(x 3)(x 5)
5x
3x
15
The reverse of this process is called
factoring. Writing a trinomial as a product of
two binomials is called factoring.
(x 3)(x 5)
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Factor
Since the lead coefficient is 1, we need two
numbers that multiply to 28 and add to 12.
Factors of -28 -1,28 1,-28 -2,14 2,-14 -4,7 4,-7
Sum of Factors 27 -27 12 -12 3 -3
Therefore
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Factor the expression
(x-3)(x7)
Cannot be factored
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Factoring a Trinomial when the lead coefficient
is not 1.
Factor
We need a combination of factors of 3 and 10 that
will give a middle term of 17. Our approach
will guess and check. Here are some possible
factorizations
This is the factorization we seek.
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Special Factoring Patterns you should remember
Pattern Name Pattern
Example
Difference of Two Squares
Perfect Square Trinomial
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Factor the quadratic expression
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A monomial is an expression that has only one
term. As a first step to factoring, you should
check to see whether the terms have a common
monomial factor.
Factor
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You can use factoring to solve certain quadratic
equation. A quadratic equation in one variable
can be written in the form
where
This is called the standard form of the equation
If this equation can be factored then we can use
this zero product property.
Zero Product Property
Let A and B be real number or algebraic
expressions. If AB 0 the either A0 or B0
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Solve
So, either (x6)0
x -6
Or (x 3)0
x 3
The solutions are 6 and 3.
These solutions are also called zeros of the
function
Notice the zeros are the x-intercepts of the
graph of the function.