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/
