Question

factor completely.\\(6r^{5} - 3r^{2} + 9r^{4} - 2r^{3}\\)

Explanation:

Step1: Rearrange terms by degree

$9r^4 + 6r^5 - 2r^3 - 3r^2$

Step2: Group terms for factoring

$(9r^4 + 6r^5) + (-2r^3 - 3r^2)$

Step3: Factor GCF from each group

$3r^4(3 + 2r) - r^2(2r + 3)$

Step4: Factor out common binomial

$(2r + 3)(3r^4 - r^2)$

Step5: Factor GCF from second term

$(2r + 3)r^2(3r^2 - 1)$

Step6: Write fully factored form

$r^2(2r + 3)(3r^2 - 1)$

Answer:

$r^2(2r + 3)(3r^2 - 1)$