Find the Holes in the Graph f(x)=(x^2-7x)/(x^2-17x+72)

$f (x) = \frac{x^{2} - 7 x}{x^{2} - 17 x + 72}$

Step 1

Factor $x$ out of $x^{2} - 7 x$ .

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

$f (x) = \frac{x \cdot x - 7 x}{x^{2} - 17 x + 72}$

Factor $x$ out of $- 7 x$ .

$f (x) = \frac{x \cdot x + x \cdot - 7}{x^{2} - 17 x + 72}$

Factor $x$ out of $x \cdot x + x \cdot - 7$ .

$f (x) = \frac{x (x - 7)}{x^{2} - 17 x + 72}$

Step 2

Factor $x^{2} - 17 x + 72$ 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 $72$ and whose sum is $- 17$ .

$- 9, - 8$

Write the factored form using these integers.

$f (x) = \frac{x (x - 7)}{(x - 9) (x - 8)}$

Step 3

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

No holes

Step 4

Find the Holes in the Graph f(x)=(x^2-7x)/(x^2-17x+72)

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