Tic Tac Toe Factoring m3f6e
This document was ed by and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this report form. Report 3b7i
Overview 3e4r5l
& View Tic Tac Toe Factoring as PDF for free.
More details w3441
- Words: 880
- Pages: 17
Tic-Tac-Toe Factoring A graphic organizer approach to factoring 2nd degree trinomials
© D. T. Simmons, 2005
1
Tic-tac-toe Factoring •
If you have been having a little bit of trouble with factoring trinomials, this graphic organizer, based on a common tic-tac-toe grid, may be just what you need.
•
To get the most out of this presentation, use pencil and paper and work through the instructions slowly and carefully.
•
Keep in mind that tic-tac-toe will not do the factoring for you. But it will keep everything organized so you can concentrate on the numbers.
•
I hope it helps. Have fun!
© D. T. Simmons, 2005
2
Step 1 •
Draw a tic-tac-toe grid with an extra box at the bottom right.
© D. T. Simmons, 2005
3
Step 2 •
Arrange the three of the trinomial in the boxes as shown.
ax ax
2
2
+ bx + c c
bx
© D. T. Simmons, 2005
4
Step 3 •
In the upper right box corner put the product of ax2 and c.
ax ax
2
2
+ bx + c c
ax 2 c
bx
© D. T. Simmons, 2005
5
Step 4 •
Now we will put some numbers in and work through the process.
ax
© D. T. Simmons, 2005
2
c
ax 2 c
6
Step 4 •
•
Now we will put some numbers in and work through the process. Use the trinomial 8x2 – 14x + 3 and set it up as shown.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
-14 x
© D. T. Simmons, 2005
7
Step 4 •
Now we will put some numbers in and work through the process.
•
Use the trinomial 8x2 – 14x + 3 and set it up as shown.
•
that the term in the upper right box is the product of the in the left and middle boxes.
© D. T. Simmons, 2005
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
-14 x
8
Step 5 •
•
Now find a pair of factors for the value of ax2c that will add up to bx. Put these two factors into the two boxes in the right column.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2 -12 x -2 x -14 x
© D. T. Simmons, 2005
9
Step 6 •
•
Now find a pair of factors for the middle term of the right column that will also be factors of ax2 and c. Be sure to watch the signs of the factors.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
4x
-3
-12 x -2 x -14 x
© D. T. Simmons, 2005
10
Step 7 •
Now do the same for the bottom term of the right column.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
11
Step 8 • •
Now all the boxes of the tictac-toe grid are filled in. Check that the two bottom of the first column are factors of the top term.
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
12
Step 8 • •
•
Now all the boxes of the tictac-toe grid are filled in.
8 x 2 - 14x + 3 ax
2
+ bx + c
Check that the two bottom of the first column are factors of the top term.
8x2
3
24 x 2
Do the same for the in the middle column.
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
13
Step 9 •
The trinomial is now factored. Each pair of diagonal is a binomial.
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
14
Step 9 •
•
The trinomial is now factored. Each pair of diagonal is a binomial. Here are the two factors of the trinomial: (4x – 1) (2x – 3)
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
15
Step 9 •
•
The trinomial is now factored. Each pair of diagonal is a binomial. Here are the two factors of the trinomial: (4x – 1) (2x – 3) Therefore:
x
1 3 and/or x 4 2
© D. T. Simmons, 2005
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
16
Try it. You’ll like it! That’s all folks!
© D. T. Simmons, 2005
17
© D. T. Simmons, 2005
1
Tic-tac-toe Factoring •
If you have been having a little bit of trouble with factoring trinomials, this graphic organizer, based on a common tic-tac-toe grid, may be just what you need.
•
To get the most out of this presentation, use pencil and paper and work through the instructions slowly and carefully.
•
Keep in mind that tic-tac-toe will not do the factoring for you. But it will keep everything organized so you can concentrate on the numbers.
•
I hope it helps. Have fun!
© D. T. Simmons, 2005
2
Step 1 •
Draw a tic-tac-toe grid with an extra box at the bottom right.
© D. T. Simmons, 2005
3
Step 2 •
Arrange the three of the trinomial in the boxes as shown.
ax ax
2
2
+ bx + c c
bx
© D. T. Simmons, 2005
4
Step 3 •
In the upper right box corner put the product of ax2 and c.
ax ax
2
2
+ bx + c c
ax 2 c
bx
© D. T. Simmons, 2005
5
Step 4 •
Now we will put some numbers in and work through the process.
ax
© D. T. Simmons, 2005
2
c
ax 2 c
6
Step 4 •
•
Now we will put some numbers in and work through the process. Use the trinomial 8x2 – 14x + 3 and set it up as shown.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
-14 x
© D. T. Simmons, 2005
7
Step 4 •
Now we will put some numbers in and work through the process.
•
Use the trinomial 8x2 – 14x + 3 and set it up as shown.
•
that the term in the upper right box is the product of the in the left and middle boxes.
© D. T. Simmons, 2005
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
-14 x
8
Step 5 •
•
Now find a pair of factors for the value of ax2c that will add up to bx. Put these two factors into the two boxes in the right column.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2 -12 x -2 x -14 x
© D. T. Simmons, 2005
9
Step 6 •
•
Now find a pair of factors for the middle term of the right column that will also be factors of ax2 and c. Be sure to watch the signs of the factors.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
4x
-3
-12 x -2 x -14 x
© D. T. Simmons, 2005
10
Step 7 •
Now do the same for the bottom term of the right column.
8 x 2 - 14x + 3 ax 2 8x2
c 3
ax 2 c 24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
11
Step 8 • •
Now all the boxes of the tictac-toe grid are filled in. Check that the two bottom of the first column are factors of the top term.
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
12
Step 8 • •
•
Now all the boxes of the tictac-toe grid are filled in.
8 x 2 - 14x + 3 ax
2
+ bx + c
Check that the two bottom of the first column are factors of the top term.
8x2
3
24 x 2
Do the same for the in the middle column.
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
13
Step 9 •
The trinomial is now factored. Each pair of diagonal is a binomial.
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
14
Step 9 •
•
The trinomial is now factored. Each pair of diagonal is a binomial. Here are the two factors of the trinomial: (4x – 1) (2x – 3)
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
© D. T. Simmons, 2005
15
Step 9 •
•
The trinomial is now factored. Each pair of diagonal is a binomial. Here are the two factors of the trinomial: (4x – 1) (2x – 3) Therefore:
x
1 3 and/or x 4 2
© D. T. Simmons, 2005
8 x 2 - 14x + 3 ax
2
+ bx + c
8x2
3
24 x 2
4x
-3
-12 x
2x
-1
-2 x -14 x
16
Try it. You’ll like it! That’s all folks!
© D. T. Simmons, 2005
17
Related Documents 3m3m1z
Tic Tac Toe Factoring m3f6e
December 2019 27
Tic-tac-toe 1k6z72
December 2019 29
Rhyming Tic Tac Toe 352e3u
November 2022 0
Tic Tac Toe 5d4e25
March 2021 0
Tic Tac Toe Game 5o1v
November 2019 39
Tic Tac Toe 5d4e25
April 2022 0More Documents from "smsalgebra" 86e4i