Factor completely 2x2 + 4x - 2.
wrong yet again!
(x + 1)(x - 1) = x^2 - 1
To factor the expression 2x^2 + 4x - 2 completely, follow these steps:
Step 1: Find the greatest common factor (GCF) of all the terms, if possible.
In this case, the GCF is 2. Divide each term by 2:
2x^2 ÷ 2 = x^2,
4x ÷ 2 = 2x, and
-2 ÷ 2 = -1.
Step 2: Write the expression using the factored GCF.
The expression becomes 2(x^2 + 2x - 1).
Step 3: Factor the quadratic trinomial inside the parentheses.
This can be done by finding two numbers whose product is -1 and whose sum is 2. The numbers are 1 and -1. Rewrite the middle term using these numbers:
x^2 + 2x - 1 = x^2 + x + x - 1.
Step 4: Group the terms in pairs and factor by grouping.
Group the first two terms together (x^2 + x) and the last two terms together (+x - 1).
Factor out the greatest common factor from each group:
x(x + 1) + (x - 1).
Step 5: Factor out the common binomial factor.
The common binomial factor is (x + 1). Factor it out:
(x + 1)(x + 1) + (x - 1) = (x + 1)(x + 1) - (x - 1).
So, the completely factored form of 2x^2 + 4x - 2 is (x + 1)(x + 1) - (x - 1), also written as (x + 1)^2 - (x - 1).
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)
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)