Download Math III

Math III: Unit 2, Lesson 2
Factoring Fanatic PowerPoint
Adapted from Factoring Fanatic Lesson
by Leah Drauch
West Point Middle School
Cullman, Alabama
Tic-Tac-But No Toe
Part 1: In the following tic-tac’s there are four numbers. Find the
relationship that the two numbers on the right have with the two
numbers on the left.
-90
10
36 -6
1
-9
-12 -6
-49
7
120
0
-7
-72
21
-36 -6
-30
-6
-6
-3
0
6
-1
5
-1
2
30
-81
9
24
-6
49
-7
34
4
0
-9
-10
-4
-14
-7
24
16
4
-3
8
4
1.
2.
What did you find?
Did it follow the pattern every time?
Tic-Tac-But No Toe
Part 2: Use your discoveries from Part 1 to complete
the following Tic-Tac’s.
9
16
18
6
-35
10
-10
9
7
2
4
45
6
-3
-15
-5
14
-5
-2
2
72
-6
-72
-36
-22
-38
-5
-1
5
9
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?
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 TicTac.
 Play the game! Just like the previous
problems. (Find the relationship!)
Once you have completed your Tic-Tac,
WHERE’S 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).
EXAMPLES
X2 – X – 12
-12 ?
-1
-12 3
-1
-4
?
What 2 numbers
complete the Tic-Tac?
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).
EXAMPLES
3X2 + 5X = 12
*Remember to
re-write in
standard form
3X2 + 5X - 12
-36 9
5
-4
-36 ?
5
?
What 2 numbers
complete the Tic Tac?
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).
EXAMPLES
2X2 + 8X - 64
*Remember that
What 2 numbers
-32 ?
sometimes a GCF
complete the Tic Tac?
should be factored
4
?
out before beginning.
2(X2 + 4X – 32)
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).
EXAMPLES
-12 ?
1
-12
-3
1
4
?
What 2 numbers
complete the Tic Tac?
Since a = 1, put a 1 in for the
numerator in two fractions.