Two students, Ann and Max, factored the trinomial 4x2-6x - 4. Ann factored it as 2 (k 2xx + 1) and Max factored it as (-2) 4x+2), Indicate which student factored the trinomial completely and which student did not, and explain why.

Given trinomial 4x^2-6x-4.

In order to factor a trinomial, we need to factor out greatest common factor (GCF).

In the given trinomial, we have terms 4x^2, - 6x, - 4.

We can see that all terms can be divided by a greatest number 2.

Therefore, greatest common factor would be 2 there.

We need to factor out 2 first.

On factoring out 2, we get

2 (2x^2 - 3x - 2).

Now, we need to factor out trinomial 2x^2 - 3x - 2 now.

We can factor a trinomial by applying product sum rule.

We have a=2, b=-3, c=-2.

ac = 2*-2 = - 4 and b=-3.

So, we need to find the factors of - 4 that add upto - 3.

Factors of - 4 would be - 4 and 1.

Let us replace - 3x by - 4x + 1x in 2x^2 - 3x - 2 trinomial

2x^2 - 3x - 2 could be rewrite as 2x^2 - 4x + 1x - 2.

Making it into two groups and factoring out GCF of each group.

We get

(2x^2 - 4x) + (1x - 2)

2x (x-2) + 1 (x-2)

= (x-2) (2x+1)

Therefore, final factors of the trinomial is 2 (x-2) (2x+1).

So, Ann factored form 2 (x-2) (2x+1) is correct.