(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Factor this quadratic expression completely.

126x² - 15x - 66

2. Relevant equations

3. 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.

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# Homework Help: Factoring quickly

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