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carmicheal · Mar 2, 2009, 08:57 PM

5x squared - 15

what is a simple way to explain how to solve this factor

ROLCAM · Mar 2, 2009, 10:00 PM

5x squared equals 15

what is a simple way to explain how to solve this factor?

The answer is THE SQUARE ROOT OF THREE.

15/5 = 3
The square root of 3 = 1.732

KISS · Mar 2, 2009, 10:13 PM

Hey, that's not factoring.

A simple way. Maybe. Take the 5 and try to divide evenly by all the prime numbers from 2 to 5. The only one is 5.

Take the 15 and do the same; all the primes from 2 through 15. Divinding by 3 gives you (3)(5)=15.

Now turn that eqn into:

5x^2-(3)(5)

Now take the common numbers out:

5(x^2-3)

done.

That method takes too long, so you have to learn how to do it my inspection. Knowing multiplication tables helps. Knowing that even numbers are divisable by 2. Any number ending in 5 is divisable by 5. If there are 2 digits and they add up to 9, then it's divisable by 9.

galactus · Mar 3, 2009, 05:38 AM

K.I.S.S. showed a nice way to go about it. But if I may give my two cents, you could note that what is in the parentheses is the difference of two squares as well and go further.

$x^{2}-3=(x+\sqrt{3})(x-\sqrt{3})$

They may not want you to go that far though.

So, we eventually get:

$5(x+\sqrt{3})(x-\sqrt{3})$