Question

factor.
$6r^3s^4 - 30r^2s^5$

$6r^3s^4 - 30r^2s^5 = \square$
(factor completely.)

Explanation:

Step1: Find the GCF of coefficients and variables

For coefficients 6 and 30, GCF is 6. For \(r\) terms: \(r^3\) and \(r^2\), GCF is \(r^2\). For \(s\) terms: \(s^4\) and \(s^5\), GCF is \(s^4\). So GCF is \(6r^2s^4\).

Step2: Divide each term by GCF

Divide \(6r^3s^4\) by \(6r^2s^4\) to get \(r\). Divide \(-30r^2s^5\) by \(6r^2s^4\) to get \(-5s\).

Step3: Write factored form

Factor out GCF: \(6r^2s^4(r - 5s)\)

Answer:

\(6r^2s^4(r - 5s)\)