Here we have some factoring that we're going to do and I'll show you the EASIEST way that I learned how to do it. It's real simple actually if you know your multiplication tables and stuff.
~*♥*~ Example 1 ~*♥*~
y² - 6y + 9
This is what I call the factoring X.
When you use the Factoring X, be sure that you put the numbers in the correct spaces or else your problem will turn out lookin' funky.
The largest number, or the last number in the equation goes on top, while the smaller number goes n bottom. Now, the two numbers on the left and right are the "factors" of 9 and -6.
For instance, -3 x -3 gives you a positive 9, and -3 + -3 gives you -6. So there you go!
So the answer would be (x-3) (x-3).
Simple as Jack <--- If you've ever watched Tropic Thunder you might find that funny. (lol Simple Jack...lol)
Answer: (x-7) (x+4)
y² - 6y + 9
This is what I call the factoring X. When you use the Factoring X, be sure that you put the numbers in the correct spaces or else your problem will turn out lookin' funky.
The largest number, or the last number in the equation goes on top, while the smaller number goes n bottom. Now, the two numbers on the left and right are the "factors" of 9 and -6.
For instance, -3 x -3 gives you a positive 9, and -3 + -3 gives you -6. So there you go!
So the answer would be (x-3) (x-3).
Simple as Jack <--- If you've ever watched Tropic Thunder you might find that funny. (lol Simple Jack...lol)
~*♥*~ Example 2 ~*♥*~
x² - 3x - 28
The factors of -28 and -3 would be -7 and 4, because -7 x 4 gives you -28 and -7 + 4 gives you -3. x² - 3x - 28
Answer: (x-7) (x+4)
~*♥*~ Example 3 ~*♥*~
x² + 3x - 10
5 x -2 = -10
5 + (-2) = 3
Answer: (x+5) (x-2)
And that would be how you do factoring my dear friends. It's simple and it's just about the only thing that I can do very well in Algebra II because it's my favorite. I could factor all day.
Oh wait, I forgot something. When you have and equation with a number in front of the variable like so:
6x² - 5x - 25
All you have to do is multiply the number in FRONT of the variable by the last number in the equation.
Now rewrite the equation:
and instead of putting -25 in the Factoring X, you put in -150 and -5. Then you find it's factors, which are 15 and -10. Then, you put all of it in the Factoring X!
And you get (x+15) (x-10), but you aren't finished, because that's not the answer. You still have the 6 that you multiplied by -25 to get the -150. So with that being the case, you have to DIVIDE (x+15) and (x-10) by 6 now.
It should look like this:
So now your equation should look like this:
So that one is a bit longer as far as the steps you have to get to find the answers. But it's still easy I think. If you think you need more practice, then go to the TEST YOUR STRENGTH area at the bottom.
x² + 3x - 10
5 x -2 = -10
5 + (-2) = 3
Answer: (x+5) (x-2)
And that would be how you do factoring my dear friends. It's simple and it's just about the only thing that I can do very well in Algebra II because it's my favorite. I could factor all day.
Oh wait, I forgot something. When you have and equation with a number in front of the variable like so:
6x² - 5x - 25
All you have to do is multiply the number in FRONT of the variable by the last number in the equation.
Now rewrite the equation:
x² - 5x -150
and instead of putting -25 in the Factoring X, you put in -150 and -5. Then you find it's factors, which are 15 and -10. Then, you put all of it in the Factoring X!
And you get (x+15) (x-10), but you aren't finished, because that's not the answer. You still have the 6 that you multiplied by -25 to get the -150. So with that being the case, you have to DIVIDE (x+15) and (x-10) by 6 now.
It should look like this:
So now your equation should look like this:
(6x+15) (6x-10), which is the answer.
So that one is a bit longer as far as the steps you have to get to find the answers. But it's still easy I think. If you think you need more practice, then go to the TEST YOUR STRENGTH area at the bottom.
~*♥*~ Test Your Strength ~*♥*~
Hint: If some of these can't be factored, just so so =^-^= Not tellin' ya which ones they are of course
1. 10y² - 7y -12
2. x² + 5x + 6
3. x² - 12x - 28
4. x² - 4x + 3
5. 2x² + 7x + 3
