Transcript The Walk Through Factorer

“The Walk Through Factorer”
0011 0010 1010 1101 0001 0100 1011
Ms. Trout’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 do the operation
• These questions will guide you through
each problem
• If you forget what a term is or need an
example click on the question mark
• The arrow keys will help navigate you
through
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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
• Group (put parenthesis) around the first two terms and the
last two terms
(6x³ -9x²) +(4x – 6)
• Factor out the common factor from each binomial
3x²(2x-3) + 2(2x-3)
• You should get the same expression
in your parenthesis.
• Factor the same expression out and
write what you have left
(2x-3)(3x² +2)
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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 the “Difference of
Two Squares”
• Are you binomials the “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 amount of terms is the size of the
polynomial.
• The terms are in between addition signs
(after turning all subtraction into addition)
• Binomial has 2 terms
• 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 you can factor that number out.
• Example:
3x² + 12 x + 9
Hint: (All the terms have a common factor of 3)
3 (x² +4x +3)
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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”
0011 0010 1010 1101 0001 0100 1011
Criteria:
• Two of the terms must be squares (A² & B²)
• There must be no minus sign before the A² or B²
• If we multiply 2(A)(B) we get the middle term (The
middle term can be – or +)
Rule:
A² +2AB+B² = (A+B)²
A²-2AB+B²= (A-B)²
Example:
x²+ 6x +9 = (x+3)²
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Factoring Trinomials Using
“Bottom’s Up”
0011 0010 1010 1101 0001 0100 1011
• Use “Bottom’s Up” to factor
• After “Bottoming Up”
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Click_Here
Factoring Completely
0011 0010 1010 1101 0001 0100 1011
• After you factor using “Bottom’s Up”, check
to see if your binomials are the “Difference
of Two Squares”.
• Are your binomials a “Difference of Two
Squares”?
Yes
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No
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“Bottom’s Up”
Ex:
2x²
–
7x
-4
0011 0010 1010 1101 0001 0100 1011
Mult. First
and last
terms
• Make your x and label
North and South
2(-4)=-8
Write the
middle term
-7
• Think of the factors that multiply to the
North and add to the South and
write those two numbers in the East
-8
and West
1
-8
-7
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“Bottoms Up” continued…
Ex: 2x² – 7x -4
0011 0010 1010 1101 0001 0100 1011
• Make a binomial of your east and west
(x+1) (x-8)
• Divide by your leading coefficient
(the number in front of x²)
(x+1/2) (x-8/2)
• Simplify the fraction to a whole
number if you can and if it is still a fraction bring
the bottom number up in front of the x
(2x +1)(x-4)
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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 the “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
Criteria:
• Has to be a binomial with a subtraction sign
• The two terms have to be perfect squares.
Rule:
(a²-b²) = (a+b) (a-b)
Example:
(x² -4) = (x +2) (x-2)
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After factoring using the “Difference of
Two Squares” look inside your ( ) again,
is1101
it another
“Difference of Two
0011 0010 1010
0001 0100 1011
Squares”?
Yes
No
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After factoring using the “Difference of
Two Squares” look inside your ( ) again,
0011 0010 1010 1101 0001 0100 1011
is it 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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Keep continuing to factor the “Difference
of
Two
Squares”
until
you
do
not
have
0011 0010 1010 1101 0001 0100 1011
any more “Difference of Two Squares”.
Then you have factored the problem
completely and can return home and
start your next problem.
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