If(2p+3)(p+5)=p2 +p+,whatisthevalueof++?

  (p - 1) • (5p + 3)

Step-by-step explanation: Changes made to your input should not affect the solution:

(1): "p2"   was replaced by   "p^2".  

STEP

1

:

Equation at the end of step 1

 (5p2 -  2p) -  3

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  5p2-2p-3  

The first term is,  5p2  its coefficient is  5 .

The middle term is,  -2p  its coefficient is  -2 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   5 • -3 = -15  

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   -2 .

     -15    +    1    =    -14  

     -5    +    3    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  3  

                    5p2 - 5p + 3p - 3

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

                   5p • (p-1)

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

                   3 • (p-1)

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

                   (5p+3)  •  (p-1)

            Which is the desired factorization