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 " .
____________________________________________________