Question

15x2+25x−10 
Factorize 
​

Answer 1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((3•5x2) -  25x) -  10

Pulling out like terms :

3.1     Pull out like factors :

  15x2 - 25x - 10  =   5 • (3x2 - 5x - 2)  

Trying to factor by splitting the middle term

3.2     Factoring  3x2 - 5x - 2  

The first term is,  3x2  its coefficient is  3 .

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

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   3 • -2 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1  

                    3x2 - 6x + 1x - 2

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

                   3x • (x-2)

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

                    1 • (x-2)

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

                   (3x+1)  •  (x-2)

            Which is the desired factorization

Final result :

 5 • (x - 2) • (3x + 1)

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