Transcript The Walk Through Factorer

“The Walk Through Factorer”
0011 0010 1010 1101 0001 0100 1011
Mrs. Pop’s!
8th Grade Algebra 1
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Directions:
0011 0010 1010 1101 0001 0100 1011
• As you work on your factoring problem,
answer the questions and follow the
necessary steps
• These questions will guide you through
each problem
• If you need help, click on the question mark
• The arrow keys will help navigate you
through your factoring adventure!
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Click on the size of your polynomial
0011 0010 1010 1101 0001 0100 1011
Binomial
Trinomial
Four Terms
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4 Terms: Factor by “Grouping”
Ex: 6x³ -9x² +4x - 6
0011 0010 1010 1101 0001 0100 1011
• Put all of the factors in a “box”
• Factor out the greatest common factor of
each row and column of the box
• Your answer will be the binomial across the
top, multiplied by the binomial down the
side.
• Check your answer by foiling
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Factoring 4 terms
0011 0010 1010 1101 0001 0100 1011
• Factor by “Grouping”
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• After factor by “Grouping” Click_Here
Factoring Completely
0011 0010 1010 1101 0001 0100 1011
• After factor by “Grouping” check to see if
your binomials are a “Difference of
Two Squares”
• Are your binomials a “Difference of Two
Squares”?
Yes
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No
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How do you determine the size of a
polynomial?
0011 0010 1010 1101 0001 0100 1011
• The number of terms determines the size of
the polynomial
• The terms are connected by addition or
subtraction signs
• A binomial has 2 terms
• A trinomial has 3 terms
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Can you factor out a common
factor?
0011 0010 1010 1101 0001 0100 1011
Yes
No
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How can you tell if you can factor
out a common factor?
0011 0010 1010 1101 0001 0100 1011
• If all the terms are divisible by the same
number and/or variable, you can factor that
number and/or variable out.
• Example:
3x² + 12 x + 9
Hint: (All the terms have a common factor of 3)
3 (x² +4x +3)
(make sure it’s the GCF!)
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Can you factor out a common
factor?
0011 0010 1010 1101 0001 0100 1011
Yes
No
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Is it a “Perfect Square Trinomial”?
0011 0010 1010 1101 0001 0100 1011
Yes
No
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“Perfect Square Trinomial”
• The
first
and0001
last0100
terms
must
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1010
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1011
be positive, perfect squares
• Multiplying 2 or -2 by the product of the square roots of
the first and last terms, will produce the middle term
• The answer will look like this (a + b)2 or (a - b)2
Example:
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x²+ 6x +9 =…the first and last terms are both positive, perfect
squares, and…
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2(x)(3) = 6x …therefore, we have a perfect square trinomial
and it is factored as the square root of the first term + the
square root of the last term, quantity squared
(x+3)²
Factoring Trinomials Using
“Diamond” or “Box and Diamond”
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• Use “Diamond or “Box and Diamond” to
factor
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• After “Doing the Diamonds”
Click_Here
Factoring Completely
0011 0010 1010 1101 0001 0100 1011
• After you factor using “Diamond” or “Box
and Diamond,” check to see if either of
your binomials are a “Difference of Two
Squares”.
• Are your binomials a “Difference of Two
Squares”?
Yes
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No
“Box and Diamonds”…the hard
ones!
0011 0010 1010 1101 0001 0100 1011
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Ex: 3x + 17x + 10
Draw a box put the first and last
term diagonal from each other
Then multiply the coefficients
together and this will give you the
number for the north
The coefficient of the middle term is
in the south
Think of the factors that multiply to
the give you the North and add to
give your the South. Write those
two numbers in the East and West
Put those same two terms in your
box multiplied by the variable
Now factor out the greatest common
factor from each row and column
The answer is (3x + 2)(x + 5)
30
15
2
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17
x
+5
3x 3x2
15x
+2 2x
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“Box and Diamond”
continued…
0011 0010 1010 1101 0001 0100 1011
• Remember, if the coefficient of the first term is
“1,” you only need to do the diamond.
• In the “north,” put the coefficient of the last term
• In the “south,” put the coefficient of the middle
term
• In the “east” and “west” go the numbers that
multiply to give you the “north” and
add to give you the “south.”
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Can you factor out a common
factor?
0011 0010 1010 1101 0001 0100 1011
Yes
No
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Is it a “Difference of Two Squares”?
0011 0010 1010 1101 0001 0100 1011
Yes
No
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“Difference of Two Squares”
0011 0010 1010 1101 0001 0100 1011
• Must be two perfect squares connected by a
subtraction sign
Rule:
(a²-b²) = (a+b) (a-b)
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Example:
(x² -4) = (x +2) (x-2)
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After factoring using
“Difference of Two Squares”
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1010 inside
1101 0001 your
0100 1011
look
( ) again. Do you have
another
“Difference of Two Squares”?
Yes
No
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After factoring using the
“Difference of Two Squares”
0011 0010
1010 1101
0001 0100
1011
look
inside
your
( ) again. Do you have
another
“Difference of Two Squares”?
Yes
No
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Congratulations
0011 0010 1010 1101 0001 0100 1011
You have completely factored your
polynomial! Good Job!
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Click on the home button to start the next
problem!
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Once your problem doesn’t contain any
additional
factors
that
are
a
“Difference
0011 0010 1010 1101 0001 0100 1011
of Two Squares,” you have factored the
problem completely and can return
home and start your next problem.
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