Question

factor.
125r² - 180
select the correct choice below and, if necessary, fill in the answer box within your choice.
a. 125r² - 180 =

b. the polynomial is prime.

Explanation:

Step1: Factor out GCD

Identify greatest common divisor (GCD) of 125 and 180, which is 5.
$125r^2 - 180 = 5(25r^2 - 36)$

Step2: Recognize difference of squares

$25r^2 - 36$ is a difference of squares: $a^2 - b^2$ where $a=5r$, $b=6$.
$25r^2 - 36 = (5r)^2 - 6^2$

Step3: Apply difference of squares formula

Use $a^2 - b^2=(a-b)(a+b)$.
$5(25r^2 - 36) = 5(5r - 6)(5r + 6)$

Answer:

A. $125r^2 - 180=5(5r - 6)(5r + 6)$