ElectricPavlov

Ooops sorry......   The remainder is of course just 70.    If you divide out the entire thing you would have a term of  70/(x+4)   i.e.

(x+4)  *  { x^2 +4x-16 + 70/(x+4)  }  = x^3 + 8x^2 +6            sorry I took it toooo far ! 

You're welcome !   ( I wasn't signed in before when I posted)

Here is one way (do not know if this is remainder theorem though)

f(x) = g(x+1) - g(x-1)

f(1/2) = g (1 1/2) - g (-1/2)

         =    1 - -1 = 2

f(-1/2) = g(-1/2 + 1) - g(-1/2-1)

            = g(1/2) - g(-1 1/2)

            =    1      -   -1  = 2

f(1/2) + f(-1/2) = 2 + 2  = 4 

2) is   4³

You are welcome......   you will learn a lot about   ln   log    e    10^x   on down the road.....   

ln is the natural logarithm function     ln (e^x)  = x       the ln function should be on your computer/calculator to solve these type of questions

ln (2) = .693147181     for the left hand side of the equation

ln(e^.059t) = .059t      for the right hand side of the equation

Here is a couple:

1)  4^2 * 4^2 = 4 ^(2+2) = 4^4 = 256     You try #3

4) is   2¹ * 2² *2²    and solved similarly   #2 is also similar    4¹  * 4² 

5)  2n^4 * 5 n^4 = 10 n^6      You try  #6

 e = 2.7182818284590452    (see the 'e' on the calculator?)

So solve this for t (the years the question is asking )

11200 = 5600 e^.059t         First divide both sides by 5600

2 = e^.059t                       Now take the ln of both sides

.693147181= .059t         Now divide both sides by .059 to find t years = 11.78 years ~~ 12 years (rounded)

If x + 2 is a factor,    then   x+2 = 0    x = -2

if you sub in -2 to the parent function it should equal 0 if x +2 is a factor

f(-2)        -2       is not