Find the Holes in the Graph f(x)=(x^3-2x^2-3x)/(-14x^2+16)

$f (x) = \frac{x^{3} - 2 x^{2} - 3 x}{- 14 x^{2} + 16}$

Factor $x^{3} - 2 x^{2} - 3 x$ .

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

Factor $x$ out of $x^{3}$ .

$f (x) = \frac{x \cdot x^{2} - 2 x^{2} - 3 x}{- 14 x^{2} + 16}$

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

$f (x) = \frac{x \cdot x^{2} + x (- 2 x) - 3 x}{- 14 x^{2} + 16}$

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

$f (x) = \frac{x \cdot x^{2} + x (- 2 x) + x \cdot - 3}{- 14 x^{2} + 16}$

Factor $x$ out of $x \cdot x^{2} + x (- 2 x)$ .

$f (x) = \frac{x (x^{2} - 2 x) + x \cdot - 3}{- 14 x^{2} + 16}$

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

$f (x) = \frac{x (x^{2} - 2 x - 3)}{- 14 x^{2} + 16}$

Factor.

Factor $x^{2} - 2 x - 3$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

$f (x) = \frac{x ((x - 3) (x + 1))}{- 14 x^{2} + 16}$

Remove unnecessary parentheses.

$f (x) = \frac{x (x - 3) (x + 1)}{- 14 x^{2} + 16}$

Factor $2$ out of $- 14 x^{2} + 16$ .

Factor $2$ out of $- 14 x^{2}$ .

$f (x) = \frac{x (x - 3) (x + 1)}{2 (- 7 x^{2}) + 16}$

Factor $2$ out of $16$ .

$f (x) = \frac{x (x - 3) (x + 1)}{2 (- 7 x^{2}) + 2 (8)}$

Factor $2$ out of $2 (- 7 x^{2}) + 2 (8)$ .

$f (x) = \frac{x (x - 3) (x + 1)}{2 (- 7 x^{2} + 8)}$

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Find the Holes in the Graph f(x)=(x^3-2x^2-3x)/(-14x^2+16)

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