Subtract these polynomials. (6x3 - 4x + 5) - (2x3 - x2 + 7x - 10) = a. 4x3 + x2 - 11x + 15 b. 4x3 - x2 - 11x + 15 c. 4x3 - x2 + 3x + 15 d. 4x3 + x2 + 3x + 15

The correct answer is:   [A]:  " 4x³ + x² − 11x + 15 " .


Note:


(6x³ − 4x + 5) − (2x³ − x² + 7x − 10) ;

=  (6x³ − 4x + 5) − 1(2x³ − x² + 7x − 10) ;


Examine the following portion of the expression:

    " − 1(2x³ − x² + 7x − 10) " ; 

=  (-1 * 2x³)  − (-1 * x²) + (-1 * 7x) − (-1 * 10) ; 

=  (-2x³) − (-1x²) + (-7x) − (-10) ; 

= (-2x³)  + 1x² − 7x + 10 ; 

=   " − 2x³ + 1x² − 7x + 10 " ;

Now, bring down the other part:

 6x³  − 4x  +  5 − 2x³ + 1x² − 7x + 10 ;

Combine the "like terms" :

6x³  − 2x³ =  + 4x³ ;

− 4x − 7x =  − 11x ; 

+ 5 + 10 = + 15 ; 

and bring down the:  

+ 1x² ( which equals:  " x² ") ; 

And rewrite:

   →  " 4x³ + x² − 11x + 15 " ; 

   →  which is:  Answer choice:  [A]:  " 4x³ + x² − 11x + 15 " .