I am stumped on this question and i need serious help. please! This is precalculus?

Question

the equation:

P(x)= -4x (x-2)^2 (x+2)^3

what does it mean when they ask to "describe the behavior of the function at each x-intercept that corresponds to a repeated factor???

Answer 1

The factors are 0, 2, 2, -2, -2, -2
The repeated factors are 2 and -2.

What does the curve do at 2 and -2?
What does it do slightly above and slight below those numbers?

At 2, the curve reaches zero. At numbers near there, it nears 0 from below.

At -2, the curve reaches zero again. Numbers less than -2 are less than zero and numbers greater than -2 are greater than zero.

Answer 2

There's a single zero at x=0, a double zero at x=2 and a triple at x=-2. So at x=2, the function "turns around" like y=x² does at its vertex. At x=-2, the function kind of curves the same way y=x³ does at x=0.

Answer 3

First, you are able to desire to be attentive to 3 trig identities right here you are able to desire to be attentive to that cos(a + b) = cos(a)cos(b) - sin(a)sin(b) and cos(a-b) = cos(a)cos(b) + sin(a)sin(b) in case you subtract the 1st of those from the 2nd, you get cos(a -b) - cos(a+b) = 2sin(a)sin(b) so utilising 5 for a and 2 for b.... 2 sin(5)sin(2) = cos(3) - cos(7)