Math III: Unit 2, Lesson 2

Factoring Fanatic PowerPoint

Adapted from Factoring Fanatic Lessonby Leah Drauch

West Point Middle SchoolCullman, Alabama

Tic-Tac-But No ToePart 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

1 -9

-30 -6

-1 5

-36 -6

0 6

120 30

34 4

-72 24

21 -3

36 -6

-12 -6

-81 9

0 -9

24 -6

-10 -4

-49 7

0 -7

16 4

8 4

-6 -3

-1 2

49 -7

-14 -7

1. What did you find?2. Did it follow the pattern every time?

Tic-Tac-But No ToePart 2: Use your discoveries from Part 1 to complete

the following Tic-Tac’s.

9

10

18

9

16

-10

6

7

4

-5

45

14

6

-5

-3

-2

72

-38

-6

-5

-72

-1

-36

5

-35

2

-15

2

-22

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 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 1/2 and -3/5, your answer would be (x + 2) (3x – 5).

EXAMPLESX2 – 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).

EXAMPLES3X2 + 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).

*Remember to re-write in standard form 3X2 + 5X - 12

EXAMPLES2X2 + 8X - 64

-32 ?

4 ?

What 2 numbers complete the Tic Tac?

-32 8

4 -4

Since a = 1, put a 1 in for the numerator in two fractions.

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).

*Remember that sometimes a GCF should be factored out before beginning. 2(X2 + 4X – 32)

EXAMPLES

-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.