Solving Quadratic Equation by Factoring.ppt

Solving Quadratic Equation by Factoring

1. Solving Equations by Factoring
Definition of Quadratic Equations
Zero-Factor Property
Strategy for Solving Quadratics

2. Standard Form Quadratic
Equation
Quadratic equations can be written in the form
ax
2
+ bx + c = 0
where a, b, and c are real numbers with a  0.
Standard form for a quadratic equation
is in descending order equal to zero.
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3. Examples of Quadratic Equations
pp 1881
2

189
2
xx
25
2
y
08118
2
pp
Standard Form
0189
2
xx
025
2
y
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4. Zero-Factor Property
If a and b are real numbers
and if ab =0, then
a = 0 or
b = 0.
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5. Solve the equation (x + 2)(2x - 1)=0
•By the zero factor property we know...
•Since the product is equal to zero then one of the factors must be
zero.
0)2( x
2x
OR(2 1) 0x 
12x
2
1
2
2

x 2
1
x
}
2
1
,2{x
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6. Solve the equation. Check your answers.
0)2)(5( xx
5x
OR
02x
2x
{2,5}x
05x Solution Set
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7. Solve each equation. Check your answers.
0)35( xx
0x OR
035 x
5
3
x
}0,
5
3
{

x
0x
Solution Set
35x
5
3
5
5
x
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8. Solving a Quadratic Equation by Factoring
Step 1 Write the equation in standard
form.
Step 2 Factor completely.
Step 3 Use the zero-factor property.
Set each factor with a variable equal
to zero.
Step 4 Solve each equation produced
in step 3.
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9. Solve.
189
2
xx
0189
2
xx
0)3)(6( xx
}3,6{x
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10. Solve.
07
2
xx
0)7( xx
}7,0{x
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11. Number Of Solutions
•The degree of a polynomial
is equal to the number of
solutions.
xxx 32
23

Three solutions!!!

12. Example
x (x + 1)(x – 3) = 0
Set each of the three factors equal to 0.
x = 0 x + 1 = 0
x = -1
x – 3 = 0
x = 3
Solve the resulting equations.
Write the solution set.
x = {0, -1, 3}
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13. Solve the following equations.
1.x
2
– 25 = 0
2.x
2
+ 7x – 8 = 0
3.x
2
– 12x + 36 = 0
4.c
2
– 8c = 0
x x 5 50
x x 8 10
x x 6 60
cc( )80
5,5
8,1
6
8,0

14. 1.Get a value of zero on one side of the
equation.
2.Factor the polynomial if possible.
3.Apply the zero product property by
setting each factor equal to zero.
4.Solve for the variable.