x2+12x+35 should be written as x^2+12x+35, where "^"
denotes exponentiation.
Since the coefficient of the x^2 term is 1, we can focus on 35, finding its factors. Note that 35 = 1*35, 5*7. Also note that 5+7 = 12.
Thus, x^2+12x+35 can be re-written as (x+5)(x+7). As a check, multiply 5 and 7; you get 35, which matches the original x^2+12x+35. Then add 5x to 7x, obtaining 12x, which also matches.