Factor 5x^3-x^2-20x+4

$5 x^{3} - x^{2} - 20 x + 4$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{3} - x^{2}) - 20 x + 4$

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

$x^{2} (5 x - 1) - 4 (5 x - 1)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $5 x - 1$ .

$(5 x - 1) (x^{2} - 4)$

Step 3

Rewrite $4$ as $2^{2}$ .

$(5 x - 1) (x^{2} - 2^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$(5 x - 1) ((x + 2) (x - 2))$

Remove unnecessary parentheses.

$(5 x - 1) (x + 2) (x - 2)$