How to factor 6x+5x-56

Question

6x² 5x-56

 

Answer 1

6X^2 - 5X - 56 =                                6 * 56 = 28 *12 = 14* 24 = 7 *48 = 21*16

                                                          21 - 16 =5

              -5x        

6X^2 - 21X + 16X -56 =

 

3X (2 X - 7) +8 ( 2X - 7) = 

 

( 2X -7 ) ( 3x + 8) 

Answer 2

OK, based on the two versions you have, I'm guessing you mean

 

6x² + 5x - 56

 

You need to break down the 6 and the -56 into possible products, and then check the combinations until you find the right sum of +5x in the middle (the O and I terms of the FOIL)

 

So the 6x² can come from

 

(2x     )(3x     )   or   (6x    )(x    )

 

and in each of these, you try the factorizations of -56, like

 

1  -56

2  -28

4  -14

7  -8

8  -7

14  -4

28  -2

56  -1

 

You also need to be sure you pair them in both orders, since

 

(6x + 2)(x - 28) = 6x² -166x - 56

 

is not the same as

 

(6x - 28)(x + 2) = 6x² - 16x - 56.  

 

Go through all the possible combinations, keeping track, until you find the one that works.  If you try them all, and none of them work, then it doesn't factor!  (Hint:  this one does factor).  

 

Dr. Carl