- #1
QuarkCharmer
- 1,051
- 3
Homework Statement
Factor this quadratic expression completely.
126x² - 15x - 66
Homework Equations
The Attempt at a Solution
126x² - 15x - 66
(9x+6)(14x-11)
I'm a good ways past this subject, but I find that it always takes me longer than some to complete these problems. If the coefficients are low numbers, I can "guess and check" and get the right combination. When the coefficients get into the higher numbers I run into trouble.
I always resort to the "box" method when the factors are not really apparent, but my professor says that I should be using "guess and check" as it's much more efficient.
Here is how I would solve the problem..
126x² - 15x - 66
3(42x² -5x - 22) //factor out the GCF
Now I take 42*-22, and think of factors of that which would make the -5.
-924=(-21*44)=(-22*42)=(-33*28)
Ok, so 33-28=-5
Now I use the "box method"
42x² | 33x
-28x | -66
Factoring out the "box"
14x 11
42x² | 33x 3x
-28x | -66 -2
So now I know the sets of numbers that I can use, I just adjust the signs to work..
3(14x-11)(3x+2) or (9x+6)(14x-11)
I know that I don't have to factor out the GCF, I just did it that way to show my steps.
I am told by everyone that the "guess and check" method is much faster, easier, and generally better to use. Am I guessing-and-checking wrong or something? At least this box method is systematic, I know I will arrive at the right answer, and not based on chance.
Any other tips on how to do this would be greatly appreciated.