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.
