Question

Help please in the comment

Answer 1

How many times does it touch the x axis for a zero?

Answer 2

That will give you the degree.

Answer 3

hmm no i don't think so

Answer 4

at -5 is crosses, that gives a factor of \(x+5\)

Answer 5

it is an odd function it will go to + infi as x go + infi and

Answer 6

at \(-1\) is crosses but is flattened out for a factor of \((x+1)^3\)

Answer 7

at 3 it touches, does not cross
factor is \((x-3)^2\)

Answer 8

and at 5 is crosses for a factor of \((x-5)\)
put it all together

Answer 9

you will see the degree is odd for sure, it is 7
\[(x+5)(x+1)^2(x-3)^2(x-5)\]

Answer 10

http://www.wolframalpha.com/input/?i=%28x%2B5%29%28x%2B1%29^3%28x-3%29^2%28x-5%29