Question

Two students, Ann and Max, factored the trinomial `3x^2 -24x-27`. Ann factored it as 3(x+1)(x−9) and Max factored it as (3x+3)(x−9). Indicate which student factored the trinomial completely and which student did not, and explain why.

Answer 1

Let's start studying case by case:
 Ann:
 3x ^ 2 -24x-27
 3 (x ^ 2 -8x-9)
 3 (x + 1) (x-9)
 Note:
 (1) * (- 9) = - 9
 (1) + (- 9) = - 8
 check:
 3 (x ^ 2-9x + x-9)
 3 (x ^ 2-8x-9)
 3x ^ 2-24x-27
 She did it correctly.
 
 Max
 3x ^ 2 -24x-27
 (3x + 3) (x-9)
 note: 
 (3) * (- 9) = - 27
 (3) + (- 9) = - 6 (incorrect: the result must be -24)