Let a = x^2 + 4. rewrite the following equation in terms of a and set it equal to zero. ( x^2 + 4 )^2 +32 = 12x^2 + 48 in resulting equation what is the coefficient of the a term ? in the resulting equation what is the constant?

 In the resulting equation:  " a² - 12a + 32 = 0 " ;

  The "coefficient" of the "a" term is:  " - 12" . 

  The "constant" is:  " 32 " .


Explanation:


Let:   "a = x² + 4 " .

Given:  (x² + 4)²  + 32  =  12x² + 48  ; 


Factor:  "12x² + 48" into " (x² + 4) " ;

"12x² + 48"  =  12 (x² + 4) " ;


Given:    (x² + 4)²  + 32  =  12x² + 48 ; 

rewrite as;  "a² + 32 = 12a " ; 

Subtract "12a" from each side of the equation; 

"a² + 32 - 12a = 12a - 12a ;
 
to get:

" a² - 12a + 32 = 0 " .

The coefficient of the "a" term;  that is:

The "coefficient" of " -12a" ;  is:  "- 12" . 

The constant is:  "32" .