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.

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)