Math III: Unit 2, Lesson 2

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Math III Unit 2, Lesson 2

• Factoring Fanatic PowerPoint

Adapted from Factoring Fanatic Lesson by Leah
Drauch West Point Middle School Cullman, Alabama
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Tic-Tac-But No ToePart 1 In the following
tic-tacs there are four numbers. Find the
relationship that the two numbers on the right
have with the two numbers on the left.
-6 -3
-1 2
-90 10
1 -9
-30 -6
-1 5
-36 -6
0 6
36 -6
-12 -6
120 30
34 4
-81 9
0 -9
24 -6
-10 -4
-49 7
0 -7
49 -7
-14 -7
-72 24
21 -3
16 4
8 4
Observations
1. What did you find? 2. Did it follow the
pattern every time?
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Tic-Tac-But No ToePart 2 Use your discoveries
from Part 1 to complete the following Tic-Tacs.
9
10
18
9
16
-10
6
7
-35
2
-15
2
6
-5
-3
-2
4
-5
45
14
72
-38
-6
-5
-72
-1
-36
5
-22
9
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Observations
Did your discovery work in every case? Do the
numbers on the right always multiply and add to
produce the numbers on the left? Can you give any
explanation for this? How could this help us in
factoring?
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Finally! Factoring with a Frenzy!

• Arrange the expression in descending (or
  ascending) order. ax2 bx c 0
• Be sure the leading coefficient is positive.
• Factor out the GCF, if necessary.
• Multiply the coefficients a and c and put the
  result in quadrant II of the Tic-Tac.
• Put the coefficient b in quadrant III of the
  Tic-Tac.
• Play the game! Just like the previous problems.
  (Find the relationship!)

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Once you have completed your Tic-Tac, WHERES
the ANSWER?

• Use the a coefficient as the numerator of two
  fractions. Use the results in quadrants I and IV
  as the two denominators.
• Reduce the fractions.
• The numerator is your coefficient for x in your
  binominal and the denominator is the constant
  term.
• EXAMPLE If you get the fractions 1/2 and
  -3/5, your answer would be (x 2) (3x 5).

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EXAMPLES
X2 X 12
-12 ?
-1 ?
What 2 numbers complete the Tic-Tac?
-12 3
-1 -4
Since a 1, put a 1 in for the numerator in two
fractions.
You found 3 and -4. These are the denominators
for the two fractions. Your fractions are 1/3
and 1/4
Your answer is (x 3) (x 4).
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EXAMPLES
3X2 5X 12
Remember to re-write in standard form 3X2 5X -
12
-36 ?
5 ?
What 2 numbers complete the Tic Tac?
-36 9
5 -4
Since a 3, put a 3 in for the numerator in two
fractions.
You found 9 and -4. These are the denominators
for the two fractions. Your fractions are 3/9
1/3 and 3/4
Your answer is (x 3) (3x 4).
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EXAMPLES
2X2 8X - 64
Remember that sometimes a GCF should be factored
out before beginning. 2(X2 4X 32)
-32 ?
4 ?
What 2 numbers complete the Tic Tac?
Since a 1, put a 1 in for the numerator in two
fractions.
-32 8
4 -4
You found 8 and -4. These are the denominators
for the two fractions. Your fractions are 1/8
and 1/4.
Your answer is 2 (x 8) (x 4).
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EXAMPLES
 
 
-12 ?
1 ?
What 2 numbers complete the Tic Tac?
Since a 1, put a 1 in for the numerator in two
fractions.
-12 -3
1 4