Factored form of 2x^2-5x-12

(x - 4) • (2x + 3)

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (2x2 -  5x) -  12

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  2x2-5x-12

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -12

Step-1 : Multiply the coefficient of the first term by the constant   2 • -12 = -24

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

     -24     +    1     =    -23  

     -12     +    2     =    -10  

     -8     +    3     =    -5     That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3

                    2x2 - 8x + 3x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2x • (x-4)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-4)

Step-5 : Add up the four terms of step 4 :

                   (2x+3)  •  (x-4)

            Which is the desired factorization

Final result :

 (x - 4) • (2x + 3)

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