Factor x^2+3x-(4/x)^3-1

$x^{2} + 3 x - {(\frac{4}{x})}^{3} - 1$

Step 1

Regroup terms.

$- 1 + x^{2} + 3 x - {(\frac{4}{x})}^{3}$

Step 2

Factor $- 1$ out of $x^{2} + 3 x - {(\frac{4}{x})}^{3}$ .

Factor $- 1$ out of $x^{2}$ .

$- 1 - 1 (- x^{2}) + 3 x - {(\frac{4}{x})}^{3}$

Factor $- 1$ out of $3 x$ .

$- 1 - 1 (- x^{2}) - (- 3 x) - {(\frac{4}{x})}^{3}$

Factor $- 1$ out of $- {(\frac{4}{x})}^{3}$ .

$- 1 - 1 (- x^{2}) - (- 3 x) - ({(\frac{4}{x})}^{3})$

Factor $- 1$ out of $- 1 (- x^{2}) - (- 3 x)$ .

$- 1 - 1 (- x^{2} - 3 x) - ({(\frac{4}{x})}^{3})$

Factor $- 1$ out of $- 1 (- x^{2} - 3 x) - ({(\frac{4}{x})}^{3})$ .

$- 1 - 1 (- x^{2} - 3 x + {(\frac{4}{x})}^{3})$

Rewrite $- 1 (- x^{2} - 3 x + {(\frac{4}{x})}^{3})$ as $- (- x^{2} - 3 x + {(\frac{4}{x})}^{3})$ .

$- 1 - (- x^{2} - 3 x + {(\frac{4}{x})}^{3})$

Step 3

Apply the product rule to $\frac{4}{x}$ .

$- 1 - (- x^{2} - 3 x + \frac{4^{3}}{x^{3}})$

Step 4

Raise $4$ to the power of $3$ .

$- 1 - (- x^{2} - 3 x + \frac{64}{x^{3}})$

Step 5

Factor $- 1$ out of $- 1 - (- x^{2} - 3 x + \frac{64}{x^{3}})$ .

Rewrite $- 1$ as $- 1 (1)$ .

$- 1 (1) - (- x^{2} - 3 x + \frac{64}{x^{3}})$

Factor $- 1$ out of $- 1 (1) - (- x^{2} - 3 x + \frac{64}{x^{3}})$ .

$- 1 (1 - x^{2} - 3 x + \frac{64}{x^{3}})$

Rewrite $- 1 (1 - x^{2} - 3 x + \frac{64}{x^{3}})$ as $- (1 - x^{2} - 3 x + \frac{64}{x^{3}})$ .

$- (1 - x^{2} - 3 x + \frac{64}{x^{3}})$

Step 6

Reorder terms.

$- (- x^{2} - 3 x + \frac{64}{x^{3}} + 1)$