For the function $f (x) = x^{2} + 5 x - 36$ solve the following.
$f (x) \leq 0$
Select the correct choice below and fill in the answer box within your choice.
A. The solution is (Use a comma to separate answers as needed.)
B. The solution is
(Type your answer in interval notation.)

Answer

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Answer

Thus, the solution is $x \in [- 9, 4]$ .

Steps

Step 1 ：Factor the quadratic expression on the left side of the inequality, which gives $(x - 4) (x + 9)$ .

Step 2 ：Build a sign chart to determine the signs of the factors and the product in different intervals.

Step 3 ：From the sign chart, we can see that $x^{2} + 5 x - 36$ is less than or equal to 0 when $- 9 < x < 4$ .

Step 4 ：Also, $f (x) = 0$ at $x = 4$ and $x = - 9$ .

Step 5 ：Thus, the solution is $x \in [- 9, 4]$ .