Question

find k if x⁵¹ +2x¹⁶ +3x +k is exactly divisible by x+¹​

Answer 1

Answer:

• the polynomial is exactly divisible by x+1 means the remainder is zero.
• $x^{51} + 2x^{16} + 3x + k = 0$  
• $x + 1 = 0 => x = -1$  
• $(-1)^{51} + 2(-1)^{16} + 3 (-1) + k =0$  
• $-1 + 2(1) + 3(1) + k =0$
• $-1 + 2 +3 + k = 0$
• $4 + k = 0$  
• $k = -4 (Ans.)$  

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