Factor the given trinomial. If the trinomial cannot be factored, indicate "Not Factorable".

2x2−8x+6


The given trinomial is \( 2x^2 - 8x + 6 \).

### Step 1: Factor out the greatest common factor (GCF)
The GCF of \( 2x^2 \), \( -8x \), and \( 6 \) is 2.

\[
2x^2 - 8x + 6 = 2(x^2 - 4x + 3)
\]

### Step 2: Factor the quadratic inside the parentheses
Now, focus on factoring \( x^2 - 4x + 3 \).

We need to find two numbers that multiply to \( 3 \) (the constant term) and add to \( -4 \) (the coefficient of the middle term).

The numbers \( -1 \) and \( -3 \) work because:

\[
-1 \times -3 = 3 \quad \text{and} \quad -1 + -3 = -4
\]

So, we can factor \( x^2 - 4x + 3 \) as:

\[
x^2 - 4x + 3 = (x - 1)(x - 3)
\]

### Step 3: Final factored form
Now, include the factor of 2:

\[
2x^2 - 8x + 6 = 2(x - 1)(x - 3)
\]

Thus, the factored form of the trinomial is:

\[
2(x - 1)(x - 3)
\]

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Would you like further details or have any questions? 

Here are some related questions for you:

1. How do you factor a trinomial if there is no common factor?
2. What is the significance of the greatest common factor in factoring?
3. How do you check if a trinomial is factorable or not?
4. What are other methods to factor trinomials when simple factoring does not work?
5. How do you factor trinomials with a leading coefficient greater than 1?

**Tip**: Always check for a greatest common factor (GCF) before trying other factoring methods.

Factor the given trinomial. If the trinomial cannot be factored, indicate 'Not Factorable'. 2x^2 − 8x + 6

Learn how to factor the trinomial 2x^2 - 8x + 6 through a detailed step-by-step solution. This algebra problem covers key concepts like the Greatest Common Factor (GCF) and trinomial factoring. Ideal for students in Grades 8-10.

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