Question

factor: 5x^{2}-10x + 5

Explanation:

Step1: Factor out the greatest - common factor

First, look at the terms of the expression \(5x^{2}-10x + 5\). The GCF of \(5x^{2}\), \(-10x\) and \(5\) is \(5\). So, \(5x^{2}-10x + 5=5(x^{2}-2x + 1)\).

Step2: Factor the quadratic expression inside the parentheses

The quadratic expression \(x^{2}-2x + 1\) is in the form of \(a^{2}-2ab + b^{2}\) where \(a = x\) and \(b = 1\). According to the perfect - square formula \(a^{2}-2ab + b^{2}=(a - b)^{2}\), so \(x^{2}-2x + 1=(x - 1)^{2}\).

Answer:

\(5(x - 1)^{2}\)