Question

Factor completely 2x2 + 4x - 2.

Answer 1

wrong yet again!
(x + 1)(x - 1) = x^2 - 1

Answer 2

First, factor out the greatest common factor of 2:

2(x^2 + 2x - 1)

Then, we need to factor the quadratic trinomial inside the parentheses.

Using the AC method, we need to find two numbers that multiply to give -1 and add to give 2. Those numbers are 1 and -1.

So, we can rewrite the quadratic trinomial as:

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

Therefore, the entire expression can be factored as:

2(x + 1)(x - 1)

Answer 3

You are correct, and I apologize for the mistake in my previous response.

Using the same factoring techniques as before, we can first factor out the greatest common factor of 2:

2(x^2 + 2x - 1)

Then, we can factor the quadratic trinomial inside the parentheses using the AC method. We need to find two numbers that multiply to give -1 and add to give 2. Those numbers are 1 and -1.

So, we can rewrite the quadratic trinomial as:

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

Therefore, the entire expression can be factored as:

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