Find the Holes in the Graph 1/(3x^2+3x-18)

$\frac{1}{3 x^{2} + 3 x - 18}$

Step 1

Factor $3 x^{2} + 3 x - 18$ .

Factor $3$ out of $3 x^{2} + 3 x - 18$ .

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

$\frac{1}{3 (x^{2}) + 3 x - 18}$

Factor $3$ out of $3 x$ .

$\frac{1}{3 (x^{2}) + 3 (x) - 18}$

Factor $3$ out of $- 18$ .

$\frac{1}{3 (x^{2}) + 3 x + 3 \cdot - 6}$

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

$\frac{1}{3 (x^{2} + x) + 3 \cdot - 6}$

Factor $3$ out of $3 (x^{2} + x) + 3 \cdot - 6$ .

$\frac{1}{3 (x^{2} + x - 6)}$

Factor.

Factor $x^{2} + x - 6$ 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Write the factored form using these integers.

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

Remove unnecessary parentheses.

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

Step 2

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

No holes

Step 3

Find the Holes in the Graph 1/(3x^2+3x-18)

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