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)