Factor \( 2 x^{2}-40 x+200 \)

To factor the expression \( 2x^{2}-40x+200 \), first, notice that all the terms share a common factor of 2. We can factor that out: \[ 2(x^{2}-20x+100) \] Next, we can focus on the quadratic equation inside the parentheses. The expression \( x^{2}-20x+100 \) is a perfect square trinomial, which can be factored as: \[ (x-10)^{2} \] So, the fully factored form of the original expression is: \[ 2(x-10)^{2} \] Now you have a clear factorization that can help you easily solve related equations! For any quadratic equation, completing the square can make factoring easier by turning it into a perfect square trinomial. Always check for common factors first, as it can simplify the process dramatically. This is a common mistake: skipping the step of factoring out any common coefficients can lead to unnecessary complications later on.