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Uncover The Mystery of Factoring Complex Trinomials!

The document provides a step-by-step method for factoring complex trinomial expressions using a tic-tac-toe board. It explains that the numbers in the first and third quadrants of the board should relate to the factors, with the product of the leading coefficient and constant term in the second quadrant and the middle term coefficient in the fourth. The factors can then be found by writing the leading coefficient over the numbers in the first and third quadrants and simplifying.

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Cherry May Masias
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143 views9 pages

Uncover The Mystery of Factoring Complex Trinomials!

The document provides a step-by-step method for factoring complex trinomial expressions using a tic-tac-toe board. It explains that the numbers in the first and third quadrants of the board should relate to the factors, with the product of the leading coefficient and constant term in the second quadrant and the middle term coefficient in the fourth. The factors can then be found by writing the leading coefficient over the numbers in the first and third quadrants and simplifying.

Uploaded by

Cherry May Masias
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPT, PDF, TXT or read online on Scribd
You are on page 1/ 9

Uncover the mystery

of factoring complex
trinomials!
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 -36 -6 -30 -6

1 -9 -12 -6 0 6 -1 5

-49 7 120 30 -81 9 -24 -6

0 -7 34 4 0 -9 -10 -4

-72 24 16 4 -6 -3 49 -7

21 -3 8 4 -1 2 -14 -7

1. What did you find?


2. 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

3. Did your discovery work in every case?


4. Can you give any explanation for this?
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!)
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 ½ and
-3/5, your answer would be (x + 2) (3x – 5).
EXAMPLES
X2 – X - 12
-12 ? What 2 numbers
complete the Tic Tac?
-1 ?

Since a = 1, put a 1 in for the


-12 3 numerator in two fractions.
You found 3 and -4. These are the
-1 -4
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 -36 ? What 2 numbers
re-write in complete the Tic Tac?
standard form 5 ?
3X2 + 5X - 12
Since a = 3, put a 3 in for the
-36 9 numerator in two fractions.
You found 9 and -4. These are the
5 -4
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
sometimes a GCF -32 ? What 2 numbers
should be factored complete the Tic Tac?
4 ?
out before beginning.
2(X2 + 4X – 32)
Since a = 1, put a 1 in for the
-32 8 numerator in two fractions.
You found 8 and -4. These are the
4 -4 denominators for the two fractions.
Your fractions are 1/8 and –1/4.
Your answer is 2 (x + 8) (x – 4).
EXAMPLES
1/2X2 + 1/2X - 6
*Remember that
sometimes a GCF -12 ? What 2 numbers
should be factored complete the Tic Tac?
1 ?
out before beginning.
1/2(X2 + X – 12)
Since a = 1, put a 1 in for the
-12 -3 numerator in two fractions.
1 4 You found -3 and 4. These are the
denominators for the two fractions.
Your fractions are –1/3 and 1/4.
Your answer is ½ (x – 3) (x + 4).

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