1. “The Walk Through Factorer”
Mrs. Pop’s!
8th Grade Algebra 1

2. Directions:
As you work on your factoring problem, answer the questions and follow the necessary steps
These questions will guide you through
each problem
If you need help, click on the question mark
The arrow keys will help navigate you through your factoring adventure!

3. Click on the size of your polynomial
Binomial
Trinomial
Four Terms

4. 4 Terms: Factor by “Grouping” Ex: 6x³ -9x² +4x - 6
Put all of the factors in a “box”
Factor out the greatest common factor of each row and column of the box
Your answer will be the binomial across the top, multiplied by the binomial down the side.
Check your answer by foiling

5. Factoring 4 terms Factor by “Grouping” After factor by “Grouping”
Click_Here

6. Factoring Completely
After factor by “Grouping” check to see if your binomials are a “Difference of
Two Squares”
Are your binomials a “Difference of Two Squares”?
Yes No

7. How do you determine the size of a polynomial?
The number of terms determines the size of the polynomial
The terms are connected by addition or subtraction signs
A binomial has 2 terms
A trinomial has 3 terms

8. Can you factor out a common factor?
Yes No

9. How can you tell if you can factor out a common factor?
If all the terms are divisible by the same number and/or variable, you can factor that number and/or variable out.
Example:
3x² + 12 x + 9
Hint: (All the terms have a common factor of 3)
3 (x² +4x +3)
(make sure it’s the GCF!)

10. Can you factor out a common factor?
Yes No

11. Is it a “Perfect Square Trinomial”?
Yes No

12. “Perfect Square Trinomial”
The first and last terms must be positive, perfect squares
Multiplying 2 or -2 by the product of the square roots of the first and last terms, will produce the middle term
The answer will look like this (a + b)2 or (a - b)2
Example:
x²+ 6x +9 =…the first and last terms are both positive, perfect squares, and…
2(x)(3) = 6x …therefore, we have a perfect square trinomial and it is factored as the square root of the first term + the square root of the last term, quantity squared
(x+3)²

13. Factoring Trinomials Using “Diamond” or “Box and Diamond”
Use “Diamond or “Box and Diamond” to factor
After “Doing the Diamonds”
Click_Here

14. Factoring Completely
After you factor using “Diamond” or “Box and Diamond,” check to see if either of your binomials are a “Difference of Two Squares”.
Are your binomials a “Difference of Two Squares”?
Yes No

15. “Box and Diamonds”…the hard ones! Ex: 3x2 + 17x + 10
Draw a box put the first and last term diagonal from each other
Then multiply the coefficients together and this will give you the number for the north
The coefficient of the middle term is in the south
Think of the factors that multiply to the give you the North and add to give your the South. Write those two numbers in the East and West
Put those same two terms in your box multiplied by the variable
Now factor out the greatest common factor from each row and column
The answer is (3x + 2)(x + 5) 30 15 2 17 x +5
3x2
15x 2x 10 3x +2

16. “Box and Diamond” continued…
Remember, if the coefficient of the first term is “1,” you only need to do the diamond.
In the “north,” put the coefficient of the last term
In the “south,” put the coefficient of the middle term
In the “east” and “west” go the numbers that multiply to give you the “north” and
add to give you the “south.”

17. Can you factor out a common factor?
Yes No

18. Is it a “Difference of Two Squares”?
Yes No

19. “Difference of Two Squares”
Must be two perfect squares connected by a subtraction sign
Rule:
(a²-b²) = (a+b) (a-b)
Example:
(x² -4) = (x +2) (x-2)

20. After factoring using “Difference of Two Squares” look inside your ( ) again. Do you have another “Difference of Two Squares”?
Yes No

21. After factoring using the “Difference of Two Squares” look inside your ( ) again. Do you have another “Difference of Two Squares”?
Yes No

22. Congratulations
You have completely factored your polynomial! Good Job!
Click on the home button to start the next problem!

23. Once your problem doesn’t contain any additional factors that are a “Difference of Two Squares,” you have factored the problem completely and can return home and start your next problem.