Question

question 10 of 10
find the factorization of the polynomial below.
100x² - 20x + 1
a. (10x - 1)²
b. (50x - 1)²
c. (10x + 1)²
d. (50x + 1)²

Explanation:

Step1: Recall perfect - square formula

The perfect - square formula is $(a - b)^2=a^{2}-2ab + b^{2}$.
For the polynomial $100x^{2}-20x + 1$, we can rewrite $100x^{2}=(10x)^{2}$, $1 = 1^{2}$, and $20x=2\times(10x)\times1$.

Step2: Apply the formula

Comparing $100x^{2}-20x + 1$ with $a^{2}-2ab + b^{2}$ where $a = 10x$ and $b = 1$, we get $100x^{2}-20x + 1=(10x - 1)^{2}$.

Answer:

A. $(10x - 1)^{2}$