QQuestion
Find the value of ‘a’ if x − a is a factor of the polynomial 3x3 + x2 − ax − 81.
✓Answer
Let f(x) = 3x3 + x2 − ax − 81.
By the Factor Theorem, if x − a is a factor of f(x), then f(a) = 0.
Since x − a = 0, x = a.
Substituting x = a:
⇒ 3a3 + a2 − a(a) − 81 = 0
⇒ 3a3 + a2 − a2 − 81 = 0
⇒ 3a3 − 81 = 0
⇒ 3a3 = 81
⇒ a3 = \frac{81}{3}
⇒ a3 = 27
⇒ a3 = 33
Therefore, a = 3.
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