Find the Holes in the Graph f(x)=(x^2+10x+24)/(x^2-10x+9)

$f (x) = \frac{x^{2} + 10 x + 24}{x^{2} - 10 x + 9}$

Factor $x^{2} + 10 x + 24$ 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 $24$ and whose sum is $10$ .

$4, 6$

Write the factored form using these integers.

$f (x) = \frac{(x + 4) (x + 6)}{x^{2} - 10 x + 9}$

Factor $x^{2} - 10 x + 9$ 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 $9$ and whose sum is $- 10$ .

$- 9, - 1$

Write the factored form using these integers.

$f (x) = \frac{(x + 4) (x + 6)}{(x - 9) (x - 1)}$

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^2+10x+24)/(x^2-10x+9)

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