Question

What are the factors of 2x^2 + 5x -12?

Answer 1

Answer:

(2x - 3) • (x + 4)

Step-by-step explanation:

Step  1  :

Equation at  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  

     -6    +    4    =    -2  

     -4    +    6    =    2  

     -3    +    8    =    5

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

                    2x2 - 3x + 8x - 12

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

                   x • (2x-3)

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

                   4 • (2x-3)

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

                   (x+4)  •  (2x-3)

            Which is the desired factorization