Factoring Quadratic Expressions ax2 bx c

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Factoring Quadratic Expressionsax2 bx c
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Setting the Stage
Do you remember how to multiply these together?
(Referred to as FOIL in some books)
6x2 8x 9x 12
(2x 3)(3x 4)
6x2 x 12
How about another way?
Complete the inside of the box by multiplying the
numbers outside the box that are in the same row
and column.
9x
6x2
12
8x
? If you combine all the like terms in the box
you get the product of (2x 3) and (3x 4)
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What is Factoring?
Basically, we are going to undo FOIL. Starting
with a quadratic expression like the one below,
6x2 x 12
we are going to find two binomials that when
multiplied together give us the original
expression. In other words, we are going to start
with the expression above and try to find the
expression
(2x 3)(3x 4)
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How To Do It
Lets start with
6x2 x 12
Make a box and put the first term in the top left
and last term in the bottom right.
To find the other two numbers, heres what you
need to do
Make a table on the left side put the product
of a and c, and on the right side put b
6x2
8x
9x
12
72
1
Put these two numbers in the box ... These last
two numbers are used to get the middle term in
our original expression, so they both need a x.
Now, find TWO numbers that multiply to make 72
and add to make 1. Click the screen when you
think you have them.
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How to Do It
Once all the numbers are in the box, we need to
determine which numbers go on the outside of the
box. Instead of just staring at the box until
you magically know what to do, start by finding
the GCF of the first row.
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?
3x
?
(2x)( ? ) 6x2
6x2
8x
2x
GCF
(2x)( ? ) 8x
(3x)( ? ) 9x
9x
12
3
?
Our original expression can now be factored using
the numbers outside the box.
6x2 x 12 (3x 4)(2x 3)
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Practice Time
Try each of these on your own when finished,
click on the answer box to see if you are
correct. If you get it wrong, or you get stuck,
click on the step by step solution box.
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Answer to Practice 1
(3x 1)(x 5)
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Answer to Practice 2
(x 8)(x 4)
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Answer to Practice 3
(4x 3)(5x 2)
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Step by Step Solution to Practice 1
After the directions show up on the right, click
the screen to complete each step. Try to
complete the next step on your own before
clicking the screen. Click the screen to begin.
3x
1
Put the first term and the last term in the box
3x2
1x
x
Make a chart with ac on the left and b on the
right
Find TWO numbers that multiply to make the number
on the left and add to make the number on the
right.
5
15x
5
Put these two numbers in the box. (Be sure they
both have an x)
Find the numbers on the outside of the box. (use
the GCF of the first row)
Write your answer in factored form.
3x2 14x 5 (3x 1)(x 5)
DONE!
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Step by Step Solution to Practice 2
After the directions show up on the right, click
the screen to complete each step. Try to
complete the next step on your own before
clicking the screen. Click the screen to begin.
8
x
Put the first term and the last term in the box
x2
8x
x
Make a chart with ac on the left and b on the
right
Find TWO numbers that multiply to make the number
on the left and add to make the number on the
right.
32
4x
4
Put these two numbers in the box. (Be sure they
both have an x)
Find the numbers on the outside of the box. (use
the GCF of the first row)
Write your answer in factored form.
x2 12x 32 (x 8)(x 4)
DONE!
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Step by Step Solution to Practice 3
After the directions show up on the right, click
the screen to complete each step. Try to
complete the next step on your own before
clicking the screen. Click the screen to begin.
3
4x
Put the first term and the last term in the box
20x2
15x
Make a chart with ac on the left and b on the
right
5x
Find TWO numbers that multiply to make the number
on the left and add to make the number on the
right.
8x
6
2
Put these two numbers in the box. (Be sure they
both have an x)
Find the numbers on the outside of the box. (use
the GCF of the first row)
(8)(15)
(8) (15)
Write your answer in factored form.
20x2 23x 6 (4x 3)(5x 2)
DONE!
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