To find one factor of the quadratic expression \( 4x^2 - 8x + 4 \), let's start by factoring the expression.

First, observe that all the coefficients have a common factor of 4, so we can factor out the 4:

\[
4x^2 - 8x + 4 = 4(x^2 - 2x + 1)
\]

Next, we factor the quadratic expression inside the parentheses:

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

Therefore, the original expression can be factored as:

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

One factor of the expression \( 4x^2 - 8x + 4 \) is \( x - 1 \).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you find the other factor of a quadratic expression?
2. What is the general method for factoring a quadratic expression?
3. Can all quadratic expressions be factored over the real numbers?
4. How can the quadratic formula be used to factor a quadratic expression?
5. What are the applications of factoring quadratic expressions?

**Tip:** Always look for common factors before attempting to factor a quadratic expression. This simplifies the process.

Discover how to factor the quadratic expression 4x^2 - 8x + 4 by identifying a common factor and using the perfect square trinomial theorem. This detailed solution is ideal for students in Grades 8-10 looking to master algebraic factoring techniques.

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