Question : If $x, y,$ and $z$ are the three factors of $a^3-7a-6$, then the value of $x+y+z$ will be:
Option 1: $3a$
Option 2: $3$
Option 3: $6$
Option 4: $a$
Answer (1)
21st Jan, 2024
Correct Answer: $3a$
Solution :
Given:
$a^3-7a-6$
= $a^3-a-6a-6$
= $a(a^2-1)-6(a+1)$
= $a(a-1)(a+1)-6(a+1)$
= $(a+1)(a^2-a-6)$
= $(a+1)(a-3)(a+2)$
So, three factors x, y, z are $(a+1)(a-3)(a+2)$.
$\therefore x+y+z= (a+1)+(a-3)+(a+2)=3a$
Hence, the correct answer is $3a$.
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