Factor 4a^3-1-a^2+4a

$4 a^{3} - 1 - a^{2} + 4 a$

Step 1

Reorder terms.

$4 a^{3} - a^{2} + 4 a - 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 a^{3} - a^{2}) + 4 a - 1$

Factor out the greatest common factor (GCF) from each group.

$a^{2} (4 a - 1) + 1 (4 a - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 a - 1$ .

$(4 a - 1) (a^{2} + 1)$