Factor quadratic using the box method (where did I go wrong?)

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mickapoo

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I feel like I am going crazy. I have gone over and over this and just cannot figure out where I went wrong.

(And before you mention it, yes, I do know now that when I factored the 60, I could have used 12 and 5 as factors, and this would have given me the right answer (which for the record is (x-4)(-3x+5). But I really want to know why, what I did originally, is not correct, so I can learn from my mistake. Thank you in advance!

Here is my work:

attachment.php
 

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mickapoo said:
I feel like I am going crazy. I have gone over and over this and just cannot figure out where I went wrong.

(And before you mention it, yes, I do know now that when I factored the 60, I could have used 12 and 5 as factors, and this would have given me the right answer (which for the record is (x-4)(-3x+5). But I really want to know why, what I did originally, is not correct, so I can learn from my mistake. Thank you in advance!

Here is my work:

attachment.php
Click to expand...
The entry in the box of row 2, column 1 should be 3x - instead of "-3x".
 
I forgot to factor out the negative 1 leading coefficient and change all the signs in step 1. So that's where I went wrong... thank you!
 
mickapoo said:
(And before you mention it, yes, I do know now that when I factored the 60, I could have used 12 and 5 as factors, and this would have given me the right answer....
Click to expand...
You have -3x2 + 17x - 20, so a = -3, b = +17, and c = -20. You have correctly multiplied ac to get ac = (-3)(-20) = +60. So the factors you're looking for must have the same sign! However, you then use factors -3 and +20. Why? ;)
 
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