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}}} 
<pre><font size = 4 color = "indigo"><b>
We must insert a +{{{0x}}}

{{{f( x ) = -4x^3 + 5x^2 + 0x+8}}} 


-2|-4  5    0   8
  |<u>    8  -26  52</u>
   -4 13  -26  60

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

-----------------------------------------------------------------

Suppose the problem has been instead:

{{{f( x ) = -4x^3 + 5x^2 + 12}}}; {{{c = 2}}} 

We must insert a +{{{0x}}}

{{{f( x ) = -4x^3 + 5x^2 + 0x+12}}} 


 2|-4  5   0  12
  |<u>   -8  -6 -12</u>
   -4 -3  -6   0

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

To write it in the form {{{f ( x ) = (x - c) (quotient)}}}

{{{f ( x ) = (x - 2)(-4x^2-3x-6)}}}

Edwin</pre>