If x, y, z are the three factors of a3 - 7a - 6, then value of x + y + z will be
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 3a
a3 - 7a - 6
= a3 - a - 6a - 6
= a(a2 - 1) - 6(a + 1)
= a (a + 1)(a - 1) - 6(a +1)
= (a + 1)[a(a - 1) - 6)]
= (a + 1)[a2 - a - 6]
= (a + 1)[a2 - 3a + 2a - 6]
= (a + 1)[a(a - 3) + 2(a - 3)]
= (a + 1)(a - 3)(a + 2)
Let x = (a + 1), y = (a - 3) and z = (a + 2)
Therefore, x + y + z = a + 1 + a - 3 + a + 2 = 3a