9514 1404 393
Answer:
(x < -7) ∪ (x > 9)
Explanation:
The zeros of the function are the values of x that make the factors zero.
x +7 = 0 ⇒ x = -7
x -9 = 0 ⇒ x = 9
When this is expanded, we can see that the leading coefficient is positive.
x² -2x -63 > 0
This means the parabola opens upward. It will be greater than 0 for x-values to the left of the left zero, and to the right of the right zero. (It is less than zero between those values.)
The solution is x < -7 or x > 9.
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In general, for polynomial inequalities, look for the locations of the zeros. The sign of the polynomial will have the sign of the leading coefficient for values of x to the right of the right-most zero. (Here, positive for x > 9.) As you progress farther to the left along the number line, the polynomial changes sign at each zero.
Here, the polynomial becomes negative between the values x=9 and x=-7. Then it is positive again for x < -7.