Question

1. factor: 5x² - 10x + 5

Explanation:

Step1: Factor out the greatest - common factor

First, find the GCF of the coefficients 5, - 10, and 5. The GCF is 5. So, $5x^{2}-10x + 5=5(x^{2}-2x + 1)$.

Step2: Factor the quadratic expression

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

Answer:

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