Question

1. factor: 5x² - 10x + 5

Explanation:

Step1: Factor out the greatest - common factor

First, factor out 5 from the expression $5x^{2}-10x + 5$. We get $5(x^{2}-2x + 1)$.

Step2: Factor the quadratic expression inside the parentheses

The quadratic expression $x^{2}-2x + 1$ is a perfect - square trinomial of the form $(a - b)^2=a^{2}-2ab + b^{2}$, where $a = x$ and $b = 1$. So $x^{2}-2x + 1=(x - 1)^{2}$.

Answer:

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