Question

factor completely
6n³ - 24n² + n - 4
(3n - 4)(8n + 1)
(6n² + 1)(n - 4)
(6n² - 1)(n + 4)
(-3n + 4)(8n - 1)

Explanation:

Step1: Group terms for factoring

$6n^3-24n^2+n-4 = (6n^3-24n^2)+(n-4)$

Step2: Factor GCF from first group

$=6n^2(n-4)+1(n-4)$

Step3: Factor out common binomial

$=(6n^2+1)(n-4)$

Step4: Verify no further factoring

$6n^2+1$ cannot be factored over integers.

Answer:

$(6n^2+1)(n-4)$