1. p^2+8p+15

ANSWER : (p + 5) • (p + 3)

Factoring  p2+8p+15  

The first term is,  p2  its coefficient is  1 .

The middle term is,  +8p  its coefficient is  8 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant  

1 • 15 = 15  

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   8 .  

     -15    +    -1    =    -16  

     -5    +    -3    =    -8  

     -3    +    -5    =    -8  

     -1    +    -15    =    -16  

     1    +    15    =    16  

     3    +    5    =    8    

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

                    p2 + 3p + 5p + 15

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

                   p • (p+3)

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

                   5 • (p+3)

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

                   (p+5)  •  (p+3)

            Which is the desired factorization

ANSWER : (p + 5) • (p + 3)

2.  x^3-x^2-10x-8

ANSWER : (x + 2) • (x + 1) • (x - 4)

- Factoring  x2+3x+2  

- The first term is,  x2  its coefficient is  1 .

- The middle term is,  +3x  its coefficient is  3 .

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

Step-1 : Multiply the coefficient of the first term by the constant  

1 • 2 = 2

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   3.

-2 +   -1  =   -3  

-1 +   -2  =   -3  

1 +   2  =   3

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

x2 + 1x + 2x + 2

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

                   x • (x+1)

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

                   2 • (x+1)

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

                  (x+2)  •  (x+1)

            Which is the desired factorization

ANSWER : (x + 2) • (x + 1) • (x - 4)