Find the Holes in the Graph f(x)=(3x^2+8x)/(x^2+3x-10)

$f (x) = \frac{3 x^{2} + 8 x}{x^{2} + 3 x - 10}$

Factor $x$ out of $3 x^{2} + 8 x$ .

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

$f (x) = \frac{x (3 x) + 8 x}{x^{2} + 3 x - 10}$

Factor $x$ out of $8 x$ .

$f (x) = \frac{x (3 x) + x \cdot 8}{x^{2} + 3 x - 10}$

Factor $x$ out of $x (3 x) + x \cdot 8$ .

$f (x) = \frac{x (3 x + 8)}{x^{2} + 3 x - 10}$

Factor $x^{2} + 3 x - 10$ 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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Write the factored form using these integers.

$f (x) = \frac{x (3 x + 8)}{(x - 2) (x + 5)}$

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)=(3x^2+8x)/(x^2+3x-10)

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