math

 

Find the interval(s) on which f(x)>0f(x)>0 and f(x)<0f(x)<0, for

 f(x)=18(x−10)(x+4)

 f(x)=−2(x−2)(x+5)

 f(x)=18(x−2)(x+7)^2(x−17)
 

 f(x)=5(x+10)^3(x+15)^2(x−15)^4

 

Find an equation for a polynomial of degree 2 with the following properties:

1. zeros at x=1 and x=−8x
2. f(0)=64
    

 

Find an equation for a polynomial of degree 3 with the following properties:

1. zeros at x=10,x=20 and x=−5x
2. f(0)=−20000

 

Find an equation for a polynomial of degree 4 with the following properties:

1. zeros at x=6,x=12 and x=−2x
2. f(0)=−6912
3. f(x)<0 only on the interval (−2,6)

 

Find an equation for a polynomial of degree 5 with the following properties:

1. zeros at x=10, and x=−7x
2. f(0)=−19
3. f(x)>0 only on the interval (−∞,−7)

 

Find an equation for a polynomial of degree 7 with the following properties:

1. zeros at x=10,x=−7 and x=−1x
2. f(0)=4
3. f(x)<0 only on the interval (−∞,−7)