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Factor completely the trinomial below. Write each factor as a polynomial in descending order.

 

12x^2 - 32x - 12

 

Any explaination would be nice

 Sep 16, 2019
 #1
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+2

 

Factor completely the trinomial below. Write each factor as a polynomial in descending order.

 

12x^2 - 32x - 12     

 

There's a scientific way to do this, but I don't know it.  I tried to find it on the internet so I could relay the method to you, but I didn't understand it. 

 

The way I do it, the way I've always done it, is to examine the numbers, then make informed guesses. 

 

This one factors to   (12x + 4)(x – 3)   It took me three tries to find the right combinations. 

 

I knew the coefficients of the "x" numbers must multiply to 12  and the "plain" numbers without an x must multiply to –12.

So I had to find the right ones.  I don't know how I do it, but I just look at them and try a few.  It took me until the third try to get it this time.

 

When you multiply the factors, you get 12x2 – 36x + 4x – 12 ,,,, then –36x + 4x gets you the –32x   

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 Sep 16, 2019
 #2
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+3

 

Oh.  Rereading the question, I see it says factor COMPLETELY. 

So you might need to pull the 4 out of that first factor. 

This depends on what your teacher expects.

 

Instead of (12x + 4)(x – 3)   it'd be   (4)(3x + 1)(x – 3) 

 

 

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Guest Sep 16, 2019
 #3
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+1

Thank You wink

CreatorRozen  Sep 16, 2019

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