Question

Which of the following is a factor of \(x^3 - 19x + 30\)?

• A. \(x + 2\)
• B. \(x + 1\)
• C. \(x - 2\)
• D. \(x - 1\)
• E. \(x - 7\)

Answer 1

The Correct Option is C

Concept: Using
Factor Theorem:

• If \(f(a) = 0\), then \((x - a)\) is a factor

Step 1: Check \(x = 2\).
\[ f(2) = 2^3 - 19(2) + 30 = 8 - 38 + 30 = 0 \]
Step 2: Apply factor theorem.
Since \(f(2) = 0\), \((x - 2)\) is a factor.
Step 3: Option analysis.

• (A) \(x+2\): \(f(-2) \neq 0\) $\times$
• (B) \(x+1\): \(f(-1) \neq 0\) $\times$
• (C) \(x-2\): \(f(2)=0\) \checkmark
• (D) \(x-1\): \(f(1) \neq 0\) $\times$
• (E) \(x-7\): \(f(7) \neq 0\) $\times$

Conclusion:
Thus, the correct answer is
Option (C).