If f(x)=-2x^2-2x+1 and g(x)=x+1 ,find (f/g)(x)

Question

Really don;t understand at all and need help 

Answer 1

(f/g)(x) = f(x) / g(x)
 
Using synthetic division, since factoring does not seem to work,
 
 
-1 | -2    -2       1
 
              2       0
_______________
      -2     0      1
 
 
The quotient is then    -2x   with a remainder of 1.
 
To check, we multiply the quotient by the divisor.  Then add the remainder.  You should get back the dividend.
 
-2x(x + 1) + 1 = -2x² - 2x + 1

 

 

This checks out!

 

If you have any questions about the synthetic division process, please let me know.  This will come in handy in your higher lever math courses.

Answer 2

If the f(x) factors into something the same as g(x), then you can cancel:

 

f(x) = 2x²  - 2x + 1 does not factor; therefor

 

( f / g) (x) = (2x² -2x +1) / ( x + 1 )

 

that is all you can do to it

 

If you were asked to evaluate (f/g)(x) for some x, say x = 3 Then:

 

(f/g)(3) = ( 2(3²)  - 2(3) + 1) / (3 + 1)

 

           = (18 - 6 + 1 ) / 4

 

           = 13/4

 

      

Answer 3

f(x) = 2x² - 2x + 1

g(x) = x + 1

 

(f/g)(x) = f(x) / g(x)

(f/g)(x) = (-2x² - 2x + 1) / (x + 1)

(f/g)(x) = -(2x² + 2x - 1) / (x + 1)

 

Since 2x² + 2x - 1 cannot be factored (over the rationals) the fraction cannot be reduced.