SOLUTION: How many zeros does the function g(x) = 4(x + 2)^5 (x-3)^3 + 5(x-3)^4 (x+2)^4 have? What are those zeros? Please and Thank You :)

Algebra ->  Rational-functions -> SOLUTION: How many zeros does the function g(x) = 4(x + 2)^5 (x-3)^3 + 5(x-3)^4 (x+2)^4 have? What are those zeros? Please and Thank You :)      Log On


   

Question 778638: How many zeros does the function g(x) = 4(x + 2)^5 (x-3)^3 + 5(x-3)^4 (x+2)^4 have? What are those zeros?
Please and Thank You :)
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
g(x) = 4(x + 2)5(x-3)3 + 5(x-3)4(x+2)4

g(x) = (x+2)4(x-3)3[4(x+2)+5(x-3)]

g(x) = (x+2)4(x-3)3[4x+8+5x-15]

g(x) = (x+2)4(x-3)3[9x-7]

x+2=0
 x=-2 is a zero of mutipicity 4

x-3=0
 x-3 is a zero of mutipicity 3

9x-7=0
  9x=7
   x=7%2F9 is a zero of mutiplicity 1.

It has three zeros:  -2, 3 and 7%2F9

Edwin