DAT QR Factoring Shortcuts

[busupshot83]

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If given a factoring problem which does not fall into one of the three common factoring methods (common factors, difference of squares, or squares of binomials) on the DAT, couldn't you just look at the multiple choices and use common sense to determine the answer?

For instance, if given the trinomial 6x^2 + x - 70, you could find the multiple choice answer of (2x + 7)(3x - 10), and use the FOIL method to see if it checks out.

Is this wise to do on the DAT to save valuable time?

 

[Streetwolf]

Rational roots might help a little?

6 can be 1x6 or 2x3
70 can be 1x70 or 2x35 or 5x14 or 7x10

That's 8 choices...

Since we're working with just x in the middle, 1x70 and 2x35 seem a bit off. Now we're down to 4 choices. I would look at 7x10 since they are close, and also 2x3 since they are close.

And we find 10x2 = 20 and 7x3 = 21 so those are the most likely candidates. Thus the 10 goes with the 3 and the 7 goes with the 2.

Otherwise you could try -b+-sqrt(b^2-4ac) / 2a:

-1 +- sqrt(1^2 - 4(-70)(6)) / 12

= -1+-sqrt(1 + 1680) / 12
= -1+-sqrt(1681)/12
= -1+-41/12
= 40/12 and -42/12
= 10/3 and -7/2

And thus x-10/3 = 0 so 3x-10 = 0
Also x+7/2 = 0 so 2x + 7 = 0

And your factors are 3x-10 and 2x+7

 

[busupshot83]

Rational roots might help a little?

6 can be 1x6 or 2x3
70 can be 1x70 or 2x35 or 5x14 or 7x10

That's 8 choices...

Since we're working with just x in the middle, 1x70 and 2x35 seem a bit off. Now we're down to 4 choices. I would look at 7x10 since they are close, and also 2x3 since they are close.

And we find 10x2 = 20 and 7x3 = 21 so those are the most likely candidates. Thus the 10 goes with the 3 and the 7 goes with the 2.

Otherwise you could try -b+-sqrt(b^2-4ac) / 2a:

-1 +- sqrt(1^2 - 4(-70)(6)) / 12

= -1+-sqrt(1 + 1680) / 12
= -1+-sqrt(1681)/12
= -1+-41/12
= 40/12 and -42/12
= 10/3 and -7/2

And thus x-10/3 = 0 so 3x-10 = 0
Also x+7/2 = 0 so 2x + 7 = 0

And your factors are 3x-10 and 2x+7

yes, that helps, thank you. i was just looking for shortcuts.