SOLUTION: Use the Factor Theorem to determine whether x - c is a factor of the following function. Write in the form f ( x ) = (x - c) (quotient) if f( x ) = -4x^3 + 5x^2 + 8; c = -2

Algebra ->  Functions -> SOLUTION: Use the Factor Theorem to determine whether x - c is a factor of the following function. Write in the form f ( x ) = (x - c) (quotient) if f( x ) = -4x^3 + 5x^2 + 8; c = -2       Log On


   



Question 160520: Use the Factor Theorem to determine whether x - c is a factor of the following function. Write in the form f ( x ) = (x - c) (quotient) if f( x ) = -4x^3 + 5x^2 + 8; c = -2
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

Use the Factor Theorem to determine whether x+-+c is a factor of the following function. Write in the form f+%28+x+%29+=+%28x+-+c%29+%28quotient%29
if f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+8; c+=+-2

We must insert a +0x

f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+0x%2B8 


-2|-4  5    0   8
  |    8  -26  52
   -4 13  -26  60

No x-c is not a factor or the 60 remainder would have been a 0.

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Suppose the problem has been instead:

f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+12; c+=+2 

We must insert a +0x

f%28+x+%29+=+-4x%5E3+%2B+5x%5E2+%2B+0x%2B12 


 2|-4  5   0  12
  |   -8  -6 -12
   -4 -3  -6   0

x-c is a factor because the remainder is 0.

To write it in the form f+%28+x+%29+=+%28x+-+c%29+%28quotient%29

f+%28+x+%29+=+%28x+-+2%29%28-4x%5E2-3x-6%29

Edwin