Question : Simplify $x^4- 15x^3+ 15x^2- 15x + 40$; given $x = 14$.
Option 1: 0
Option 2: 40
Option 3: 14
Option 4: 26
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Correct Answer: 26
Solution : Given: $x^4- 15x^3+ 15x^2- 15x + 40$ = $14^4- 15(14)^3+ 15(14)^2- 15(14) + 40$ = $14^4- (14+1)(14)^3+ (14+1)(14)^2- (14+1)(14) + 40$ = $14^4-14^4-14^3+14^3+14^2-14^2-14+40$ = $26$ Hence, the correct answer is 26.
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