Question

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.

Answer 1

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.