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Math
A |
Solving
Factorable Quadratic Equations |
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There's
no magic to solving factorable quadratic equations. All it
takes is that you remember how to factor
algebraic expressions. |
Let's
do a quick review of factoring.
(If you need a more in depth look at factoring,
check Section 3 from the Math homepage under the Factoring topic.)
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There
are three types of factoring |
|
| *Common
Monomial |
ab
+ ac = a(b+c) |
| *Difference
of Squares |
x2-9
= (x+3)(x-3) |
| *Quadratic
Trinomial |
x2-5x+6=(x-3)(x-2) |
If you can factor, you can solve factorable quadratic equations.
Here are the steps you should follow:
| 1. |
Move
all terms to the same side, so the equation is set equal to 0. |
| 2. |
Factor
the algebraic expression. |
| 3. |
Set
each factor equal to 0.
(If the product of two factors equals 0, then either one or both of
the factors must be 0.) |
| 4. |
Solve
each resulting equation.
|
Solve
for x: x2+3x = 0
| Factor
the common monomial. |
x(x+3)=0 |
| Set
each factor equal to 0 and solve for x. |
x=0
and |
x+3=0
x = -3 |
| List
all values of x. |
x
= {0,-3} |
Solve
for y: y2 = 16
| Get
all terms on the same side. |
y2-16=0 |
| Factor
the difference of squares. |
(y+4)(y-4)=0 |
| Set
each factor equal to 0 and solve for y. |
y+4=0
and
y = -4 |
y-4=0
y = 4 |
| List
all values of y. |
y
= {-4,4} |
Solve
for c: c2-12=c
| Get
all terms on the same side. |
c2-12-c=0 |
| Arrange
the terms in standard form. |
c2-c-12=0 |
| Factor
the quadratic trinomial. |
(c+3)(c-4)=0 |
| Set
each factor equal to 0 and solve for c. |
c+3=0
and
c= -3 |
c-4=0
c= 4 |
| List
all values of c. |
c
= {-3,4} |
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How to use
your
TI-83+ graphing calculator with
factoring quadratic equations.
Click calculator. |
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