Factoring?

Question

I can not figure this question out..

 Solve the equation by factoring:

 

15x^2 + 11x - 56 = 0

 

Is this even possible?

Answer 1

I will show you a trick that solves all this kind of problems.

 

   15X² + 11X - 56 

 

    A quadratic like this can only be factorable, if  There exist 2 rational numbers whose Sum is 11, and 

   their product is  - 15 * 56

 

          So we rite 15 * 56  as product of its factor

  

            15 * 56 =  3 * 5 * 7 * 8 = 15 * 56 = 35 * 24 = 

 

                   Now we see that  the difference of 35 and 24 is 11

 

                15 X² + 35X - 24X -56   ( break up 11X into 35X- 24X)

                 

              5X( 3X +7 )  - 8 ( 3X + 7)  , Now 2 terms have common factor  of (3X +7 )

 

                ( 3X + 7 ) ( 5X - 8 )    This is the final answer. 

 

                

Answer 2

Hi Addie;

15x² + 11x - 56 = 0

 

Let's break this down...

15x²

(x)(x)=x²

(5)(3)=15 or (15)(1)=15

 

11x

11x=(11x+0x) or (10x+1x) or (9x+2x), etc

 

-56

(-8)(7) or (8)(-7)

 

Let's factor...

15x² + 11x - 56 = 0

(?x+  ??)(?x-  ??)

 

Because the 11x is positive, the added ??x must be greater than the subtracted ??x.

(3x+7)(5x-8)=0

Let's FOIL...

FIRST.....15x²

OUTER...-24x

INNER.....35x

LAST.......56

 

15x²-24x+35x+56=0

15x²+11x-56=0