Kruegs1982
07-04-2007, 11:41 PM
How do you all teach factoring? When I learned it we just had to do it and basically guess and check. This past year a teacher taught me a method to the madness called the X-box. I will try and post the method but its going to be a little difficult without being able to draw it out. Does anyone else have a method or do you teach it the old school way???
X-box:
Problem: Factor ax^2 + bx + c
1. Draw a large X.
2. In the top of the X, calculate a*c
3. in the bottom of the X write b
4. in the sides write all the factors of a*c (i.e. if it was a 2, you would write 2 in the left side of the X and 1 on the right side of the X)
5. circle the factors that add up to b
6. Draw a box
7. separate the box into 4 quadrants (we will refer to the quadrants like those on a graph)
8. In Quad. II, write ax^2
9. In Quad IV, write c
10. in Quad I and III, write the numbers you circled in step 5, along with an x.
11. to the left of Quadrant II write the GCF of Quad I and II.
12. Now it is a lot like a multiplication table, on the top of quadrant II, you ask yourself what multiplies with the GCF to get quadrant II? ETC
13. Now your factors of the polynomial are on the top of the box and along the side of the box.
Example:
factor 3x^2+5x+2
top of the x: 6
bottom of the x: 5
left and right of the x: 2 and 3
Quad II: 3x^2
Quad IV: 2
Quad I: 2x
Quad III: 3x
left of quad II: x (it's the GCF of 3x^2 and 2x)
top of quad II: 3x (because x * 3x = 3x^2)
top of quad I: 2 (because x*2=2x)
left of quad III: 1 (because 3x*1=3x)
Now on the top of your box you should have the first factor and the side of your box you should have the 2nd factor: (3x+2)(x+1)
It sounds complicated but students actually really like it and understand it
X-box:
Problem: Factor ax^2 + bx + c
1. Draw a large X.
2. In the top of the X, calculate a*c
3. in the bottom of the X write b
4. in the sides write all the factors of a*c (i.e. if it was a 2, you would write 2 in the left side of the X and 1 on the right side of the X)
5. circle the factors that add up to b
6. Draw a box
7. separate the box into 4 quadrants (we will refer to the quadrants like those on a graph)
8. In Quad. II, write ax^2
9. In Quad IV, write c
10. in Quad I and III, write the numbers you circled in step 5, along with an x.
11. to the left of Quadrant II write the GCF of Quad I and II.
12. Now it is a lot like a multiplication table, on the top of quadrant II, you ask yourself what multiplies with the GCF to get quadrant II? ETC
13. Now your factors of the polynomial are on the top of the box and along the side of the box.
Example:
factor 3x^2+5x+2
top of the x: 6
bottom of the x: 5
left and right of the x: 2 and 3
Quad II: 3x^2
Quad IV: 2
Quad I: 2x
Quad III: 3x
left of quad II: x (it's the GCF of 3x^2 and 2x)
top of quad II: 3x (because x * 3x = 3x^2)
top of quad I: 2 (because x*2=2x)
left of quad III: 1 (because 3x*1=3x)
Now on the top of your box you should have the first factor and the side of your box you should have the 2nd factor: (3x+2)(x+1)
It sounds complicated but students actually really like it and understand it