Question

F(x)= x(x+3)(x+1)(x-4) has zeros at x=-3

Answer 1

Answer:  C) Sometimes positive; sometimes negative

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Explanation:

Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5

Plug this into f(x)

f(x) = x(x+3)(x+1)(x-4)

f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)

f(-0.5) = -0.5(2.5)(0.5)(-4.5)

f(-0.5) = 2.8125

We get a positive value.

This shows that f(x) is positive on the region of -1 < x < 0

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Now pick a value between x = 0 and x = 4. I'll use x = 1

f(x) = x(x+3)(x+1)(x-4)

f(1) = 1(1+3)(1+1)(1-4)

f(1) = 1(4)(2)(-3)

f(1) = -24

Therefore, f(x) is negative on the interval 0 < x < 4

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In short, f(x) is both positive and negative on the interval -1 < x < 4

It's positive when -1 < x < 0

And it's negative when 0 < x < 4