Question

factor completely.
$36j^{5} - 18j^{4} - 6j^{3} + 3j^{2}$

Explanation:

Step1: Find the GCF of coefficients and variables

First, find the greatest common factor (GCF) of the coefficients \(36\), \(-18\), \(-6\), and \(3\). The GCF of these numbers is \(3\). For the variable part, the lowest power of \(j\) is \(j^{2}\). So the GCF of the terms is \(3j^{2}\).

Step2: Factor out the GCF

Factor out \(3j^{2}\) from each term:

$$
LATEXBLOCK0
$$

We can check if the polynomial inside the parentheses can be factored further. Let's try factoring by grouping. Group the first two terms and the last two terms:

$$
LATEXBLOCK1
$$

Now, put it all together:

$$ 36j^{5}-18j^{4}-6j^{3}+3j^{2}=3j^{2}(6j^{2}-1)(2j - 1) $$

Answer:

\(3j^{2}(6j^{2}-1)(2j - 1)\)