Can you help with this polynomial?

Question

For the polynomial p(x)=(x+2)^2 (x+3) (x-1)^3 find the following:

a) The degree of p.  (would this be 6?)

b) The y-intercept.

c) the x-intercepts.

d) The intervals where p(x)>0 and p(x)<0.

An explanation would be very helpful. I don't want just answers because I actually want to understand it. Thank you for any help. (10 points to best answer)

Hankm · Accepted Answer

yes the degree is 6

to get the y intercept solve for x = 0
 
to get the x intercepts substitute the values of the roots for x
x= -2,-3,+1

a polynomial cannot change from positive to negative without going through either zero or infinity.
since there is no denominator to this polynomial it cannot become infinity for finite x.

so regions of interest are 
-inf to -3
-3 to -2
-2 to +1
+1 to inf
the regions will alternate in sign 
to get the sign for the region from -2 to +1 lets substitute x=-1
p= (-1+2)^2*(-1+3)*(-1-1)^3
p = 1*2*(-8) = -16 so this region is negative

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Can you help with this polynomial?

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