NO LINKS OR ANSWERING IF YOU DON'T KNOW Determine the intervals where the value of f(x) is negative, when
f(x) = (x + 7)(2x - 3)(x - 5). Choose all that apply.

a. -∞ < x < -7
b. -7 < x < 3/2
c. 3/2 < x < 5
d. 5 < x < ∞

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  a, c

Step-by-step explanation:

There are 3 linear factors, so the function is odd degree (cubic). The coefficients of x are all positive, so the function has the general shape of an increasing function, left-to-right. The three linear factors mean that the curve crosses the x-axis 3 times, changing sign each time.

The x-intercepts are the values of x that make the factors zero: -7, 3/2, 5. The shape of the function tells you it will be negative for x < -7. Between -7 and 3/2, it will be positive, since it changes sign at x=-7. It changes sign again at x=3/2, so will be negative for 3/2 < x < 5.

In short, the function will be negative at any point that has an odd number of function zeros to its right (taking multiplicity into account).

The function is negative on intervals (a) and (c).