Question

Factor the expression f^2+10f+16

Answer 1

Answer:

 (f + 8) • (f + 2)

Step-by-step explanation:

Factoring  f2+10f+16  

The first term is,  f2  its coefficient is  1 .

The middle term is,  +10f  its coefficient is  10 .

The last term, "the constant", is  +16  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16  

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   10 .

     -16    +    -1    =    -17  

     -8    +    -2    =    -10  

     -4    +    -4    =    -8  

     -2    +    -8    =    -10  

     -1    +    -16    =    -17  

     1    +    16    =    17  

     2    +    8    =    10    That's it

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

                    f2 + 2f + 8f + 16

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

                   f • (f+2)

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

                   8 • (f+2)

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

                   (f+8)  •  (f+2)

            Which is the desired factorization

Source: https://www.tiger-algebra.com/drill/f~2_10f_16/

Answer 2

Answer: (f + 2) (f + 8)

It's hard to explain, but I suggest you use the AC method. Hope this helps!